x^2+20x-12=0

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Solution for x^2+20x-12=0 equation:


Simplifying
x2 + 20x + -12 = 0

Reorder the terms:
-12 + 20x + x2 = 0

Solving
-12 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 20x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 20x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 20x + x2 = 0 + 12
20x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
20x + x2 = 12

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 = 12 + 100

Reorder the terms:
100 + 20x + x2 = 12 + 100

Combine like terms: 12 + 100 = 112
100 + 20x + x2 = 112

Factor a perfect square on the left side:
(x + 10)(x + 10) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(x + 10) equal to 10.583005244 and -10.583005244.

Subproblem 1

x + 10 = 10.583005244 Simplifying x + 10 = 10.583005244 Reorder the terms: 10 + x = 10.583005244 Solving 10 + x = 10.583005244 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 = 10.583005244 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.583005244 + -10 x = 10.583005244 + -10 Combine like terms: 10.583005244 + -10 = 0.583005244 x = 0.583005244 Simplifying x = 0.583005244

Subproblem 2

x + 10 = -10.583005244 Simplifying x + 10 = -10.583005244 Reorder the terms: 10 + x = -10.583005244 Solving 10 + x = -10.583005244 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 = -10.583005244 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.583005244 + -10 x = -10.583005244 + -10 Combine like terms: -10.583005244 + -10 = -20.583005244 x = -20.583005244 Simplifying x = -20.583005244

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.583005244, -20.583005244}

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