Solve Nonlinearequations 5x^2=10 Tiger Algebra Solver

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Enter an equation or problemClear Solve × Camera input is not recognized!axy/|abs|( )789*456-%123+<>0,.=abcabcdefghijklmnopqrstuvwxyz␣.Solution - Nonlinear equations x=±(2)=±1.4142 x=±sqrt(2)=±1.4142

Other Ways to Solve

Nonlinear equations

• Solving quadratic equations using the quadratic formula
• Solving quadratic equations by completing the square

Step by Step Solution

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 5*x^2-(10)=0

Step by step solution :

Step 1 :

Equation at the end of step 1 :

5x2 - 10 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors : 5x2 - 10 = 5 • (x2 - 2)

Trying to factor as a Difference of Squares :

3.2 Factoring: x2 - 2 Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)Proof : (A+B) • (A-B) = A2 - AB + BA - B2 = A2 - AB + AB - B2 = A2 - B2Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated from the expression.Check : 2 is not a square !! Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step 3 :

5 • (x2 - 2) = 0

Step 4 :

Equations which are never true :

4.1 Solve : 5 = 0This equation has no solution. A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2 Solve : x2-2 = 0Add 2 to both sides of the equation : x2 = 2 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: x = ± √ 2 The equation has two real solutions These solutions are x = ± √2 = ± 1.4142

Two solutions were found :

x = ± √2 = ± 1.4142

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Why learn this

Terms and topics

• Nonlinear equations
• Polynomial root calculator

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