Algebra InputsTrigonometry InputsCalculus InputsMatrix Inputs Basic algebra trigonometry calculus statistics matrices CharactersSolve for t t = \frac{\sqrt{40017} + 215}{32} \approx 12.970077984 t=\frac{215-\sqrt{40017}}{32}\approx 0.467422016Steps Using the Quadratic FormulaSteps for Completing the SquareView solution stepsSteps Using the Quadratic Formula 97 = 215 t - 16 t ^ { 2 } Swap sides so that all variable terms are on the left hand side. 215t-16t^{2}=97 Subtract 97 from both sides. 215t-16t^{2}-97=0 All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction. -16t^{2}+215t-97=0 This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 215 for b, and -97 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}. t=\frac{-215±\sqrt{215^{2}-4\left(-16\right)\left(-97\right)}}{2\left(-16\right)} Square 215. t=\frac{-215±\sqrt{46225-4\left(-16\right)\left(-97\right)}}{2\left(-16\right)} Multiply -4 times -16. t=\frac{-215±\sqrt{46225+64\left(-97\right)}}{2\left(-16\right)} Multiply 64 times -97. t=\frac{-215±\sqrt{46225-6208}}{2\left(-16\right)} Add 46225 to -6208. t=\frac{-215±\sqrt{40017}}{2\left(-16\right)} Multiply 2 times -16. t=\frac{-215±\sqrt{40017}}{-32} Now solve the equation t=\frac{-215±\sqrt{40017}}{-32} when ± is plus. Add -215 to \sqrt{40017}. t=\frac{\sqrt{40017}-215}{-32} Divide -215+\sqrt{40017} by -32. t=\frac{215-\sqrt{40017}}{32} Now solve the equation t=\frac{-215±\sqrt{40017}}{-32} when ± is minus. Subtract \sqrt{40017} from -215. t=\frac{-\sqrt{40017}-215}{-32} Divide -215-\sqrt{40017} by -32. t=\frac{\sqrt{40017}+215}{32} The equation is now solved. t=\frac{215-\sqrt{40017}}{32} t=\frac{\sqrt{40017}+215}{32} QuizQuadratic Equation5 problems similar to: 97 = 215 t - 16 t ^ { 2 }
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97=215t-16t^2http://www.tiger-algebra.com/drill/97=215t-16t~2/ 97=215t-16t2 Two solutions were found : t =(215-√40017)/32= 0.467 t =(215+√40017)/32=12.970 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both ... 9a^3+15a^2-36ahttp://www.tiger-algebra.com/drill/9a~3_15a~2-36a/ 9a3+15a2-36a Final result : 3a • (3a - 4) • (a + 3) Step by step solution : Step 1 :Equation at the end of step 1 : ((9 • (a3)) + (3•5a2)) - 36a Step 2 :Equation at the end of step 2 : (32a3 ... 71=125t-16t^2http://www.tiger-algebra.com/drill/71=125t-16t~2/ 71=125t-16t2 Two solutions were found : t =(125-√11081)/32= 0.617 t =(125+√11081)/32= 7.196 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both ... 87=195t-16t^2http://tiger-algebra.com/drill/87=195t-16t~2/ 87=195t-16t2 Two solutions were found : t =(195-√32457)/32= 0.464 t =(195+√32457)/32=11.724 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both ... 93=201t-16t^2https://www.tiger-algebra.com/drill/93=201t-16t~2/ 93=201t-16t2 Two solutions were found : t =(201-√34449)/32= 0.481 t =(201+√34449)/32=12.081 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both ... (2a^3b^2)(3ab^4)^3http://www.tiger-algebra.com/drill/(2a~3b~2)(3ab~4)~3/ (2a3b2)(3ab4)3 Final result : (2•33a6b14) Step by step solution : Step 1 :Equation at the end of step 1 : ((2•(a3))•(b2))•((3ab4)3) Step 2 :Equation at the end of step 2 : (2a3 • b2) • 33a3b12 ...More Items
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CopyCopied to clipboard215t-16t^{2}=97 Swap sides so that all variable terms are on the left hand side.215t-16t^{2}-97=0 Subtract 97 from both sides.-16t^{2}+215t-97=0 All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.t=\frac{-215±\sqrt{215^{2}-4\left(-16\right)\left(-97\right)}}{2\left(-16\right)} This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 215 for b, and -97 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.t=\frac{-215±\sqrt{46225-4\left(-16\right)\left(-97\right)}}{2\left(-16\right)} Square 215.t=\frac{-215±\sqrt{46225+64\left(-97\right)}}{2\left(-16\right)} Multiply -4 times -16.t=\frac{-215±\sqrt{46225-6208}}{2\left(-16\right)} Multiply 64 times -97.t=\frac{-215±\sqrt{40017}}{2\left(-16\right)} Add 46225 to -6208.t=\frac{-215±\sqrt{40017}}{-32} Multiply 2 times -16.t=\frac{\sqrt{40017}-215}{-32} Now solve the equation t=\frac{-215±\sqrt{40017}}{-32} when ± is plus. Add -215 to \sqrt{40017}.t=\frac{215-\sqrt{40017}}{32} Divide -215+\sqrt{40017} by -32.t=\frac{-\sqrt{40017}-215}{-32} Now solve the equation t=\frac{-215±\sqrt{40017}}{-32} when ± is minus. Subtract \sqrt{40017} from -215.t=\frac{\sqrt{40017}+215}{32} Divide -215-\sqrt{40017} by -32.t=\frac{215-\sqrt{40017}}{32} t=\frac{\sqrt{40017}+215}{32} The equation is now solved.215t-16t^{2}=97 Swap sides so that all variable terms are on the left hand side.-16t^{2}+215t=97 Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.\frac{-16t^{2}+215t}{-16}=\frac{97}{-16} Divide both sides by -16.t^{2}+\frac{215}{-16}t=\frac{97}{-16} Dividing by -16 undoes the multiplication by -16.t^{2}-\frac{215}{16}t=\frac{97}{-16} Divide 215 by -16.t^{2}-\frac{215}{16}t=-\frac{97}{16} Divide 97 by -16.t^{2}-\frac{215}{16}t+\left(-\frac{215}{32}\right)^{2}=-\frac{97}{16}+\left(-\frac{215}{32}\right)^{2} Divide -\frac{215}{16}, the coefficient of the x term, by 2 to get -\frac{215}{32}. Then add the square of -\frac{215}{32} to both sides of the equation. This step makes the left hand side of the equation a perfect square.t^{2}-\frac{215}{16}t+\frac{46225}{1024}=-\frac{97}{16}+\frac{46225}{1024} Square -\frac{215}{32} by squaring both the numerator and the denominator of the fraction.t^{2}-\frac{215}{16}t+\frac{46225}{1024}=\frac{40017}{1024} Add -\frac{97}{16} to \frac{46225}{1024} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.\left(t-\frac{215}{32}\right)^{2}=\frac{40017}{1024} Factor t^{2}-\frac{215}{16}t+\frac{46225}{1024}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.\sqrt{\left(t-\frac{215}{32}\right)^{2}}=\sqrt{\frac{40017}{1024}} Take the square root of both sides of the equation.t-\frac{215}{32}=\frac{\sqrt{40017}}{32} t-\frac{215}{32}=-\frac{\sqrt{40017}}{32} Simplify.t=\frac{\sqrt{40017}+215}{32} t=\frac{215-\sqrt{40017}}{32} Add \frac{215}{32} to both sides of the equation.
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Steps Using the Quadratic FormulaSteps for Completing the SquareView solution stepsSteps Using the Quadratic Formula 97 = 215 t - 16 t ^ { 2 } Swap sides so that all variable terms are on the left hand side. 215t-16t^{2}=97 Subtract 97 from both sides. 215t-16t^{2}-97=0 All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction. -16t^{2}+215t-97=0 This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 215 for b, and -97 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}. t=\frac{-215±\sqrt{215^{2}-4\left(-16\right)\left(-97\right)}}{2\left(-16\right)} Square 215. t=\frac{-215±\sqrt{46225-4\left(-16\right)\left(-97\right)}}{2\left(-16\right)} Multiply -4 times -16. t=\frac{-215±\sqrt{46225+64\left(-97\right)}}{2\left(-16\right)} Multiply 64 times -97. t=\frac{-215±\sqrt{46225-6208}}{2\left(-16\right)} Add 46225 to -6208. t=\frac{-215±\sqrt{40017}}{2\left(-16\right)} Multiply 2 times -16. t=\frac{-215±\sqrt{40017}}{-32} Now solve the equation t=\frac{-215±\sqrt{40017}}{-32} when ± is plus. Add -215 to \sqrt{40017}. t=\frac{\sqrt{40017}-215}{-32} Divide -215+\sqrt{40017} by -32. t=\frac{215-\sqrt{40017}}{32} Now solve the equation t=\frac{-215±\sqrt{40017}}{-32} when ± is minus. Subtract \sqrt{40017} from -215. t=\frac{-\sqrt{40017}-215}{-32} Divide -215-\sqrt{40017} by -32. t=\frac{\sqrt{40017}+215}{32} The equation is now solved. t=\frac{215-\sqrt{40017}}{32} t=\frac{\sqrt{40017}+215}{32} QuizQuadratic Equation5 problems similar to: 97 = 215 t - 16 t ^ { 2 }
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