Linear Equations With One Unknown - Tiger Algebra

Step by step solution :

Step 1 :

Equation at the end of step 1 :

Step 2 :

Checking for a perfect cube :

2.1 2x3-x2+10x-5 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: 2x3-x2+10x-5 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: 10x-5 Group 2: 2x3-x2 Pull out from each group separately :Group 1: (2x-1) • (5)Group 2: (2x-1) • (x2) -------------------Add up the two groups : (2x-1) • (x2+5) Which is the desired factorization

Polynomial Roots Calculator :

2.3 Find roots (zeroes) of : F(x) = x2+5Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integersThe Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 1 and the Trailing Constant is 5. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,5 Let us test ....

Polynomial Roots Calculator found no rational roots

Equation at the end of step 2 :

Step 3 :

Theory - Roots of a product :

3.1 A product of several terms equals zero.When a product of two or more terms equals zero, then at least one of the terms must be zero.We shall now solve each term = 0 separatelyIn other words, we are going to solve as many equations as there are terms in the productAny solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

3.2 Solve : x2+5 = 0Subtract 5 from both sides of the equation : x2 = -5 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: x = ± √ -5 In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1 Accordingly, √ -5 = √ -1• 5 = √ -1 •√ 5 = i • √ 5 The equation has no real solutions. It has 2 imaginary, or complex solutions. x= 0.0000 + 2.2361 i x= 0.0000 - 2.2361 i

Solving a Single Variable Equation :

3.3 Solve : 2x-1 = 0Add 1 to both sides of the equation : 2x = 1 Divide both sides of the equation by 2: x = 1/2 = 0.500

Three solutions were found :

1. x = 1/2 = 0.500
2. x= 0.0000 - 2.2361 i
3. x= 0.0000 + 2.2361 i