x^2+20x-40=0

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Solution for x^2+20x-40=0 equation:


Simplifying
x2 + 20x + -40 = 0

Reorder the terms:
-40 + 20x + x2 = 0

Solving
-40 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 20x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 20x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 20x + x2 = 0 + 40
20x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
20x + x2 = 40

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 40 + 100

Reorder the terms:
100 + 20x + x2 = 40 + 100

Combine like terms: 40 + 100 = 140
100 + 20x + x2 = 140

Factor a perfect square on the left side:
(x + 10)(x + 10) = 140

Calculate the square root of the right side: 11.832159566

Break this problem into two subproblems by setting 
(x + 10) equal to 11.832159566 and -11.832159566.

Subproblem 1

x + 10 = 11.832159566 Simplifying x + 10 = 11.832159566 Reorder the terms: 10 + x = 11.832159566 Solving 10 + x = 11.832159566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 11.832159566 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.832159566 + -10 x = 11.832159566 + -10 Combine like terms: 11.832159566 + -10 = 1.832159566 x = 1.832159566 Simplifying x = 1.832159566

Subproblem 2

x + 10 = -11.832159566 Simplifying x + 10 = -11.832159566 Reorder the terms: 10 + x = -11.832159566 Solving 10 + x = -11.832159566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -11.832159566 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.832159566 + -10 x = -11.832159566 + -10 Combine like terms: -11.832159566 + -10 = -21.832159566 x = -21.832159566 Simplifying x = -21.832159566

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.832159566, -21.832159566}

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