x*x+12x-162=0

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Solution for x*x+12x-162=0 equation:


Simplifying
x * x + 12x + -162 = 0

Multiply x * x
x2 + 12x + -162 = 0

Reorder the terms:
-162 + 12x + x2 = 0

Solving
-162 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '162' to each side of the equation.
-162 + 12x + 162 + x2 = 0 + 162

Reorder the terms:
-162 + 162 + 12x + x2 = 0 + 162

Combine like terms: -162 + 162 = 0
0 + 12x + x2 = 0 + 162
12x + x2 = 0 + 162

Combine like terms: 0 + 162 = 162
12x + x2 = 162

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 162 + 36

Reorder the terms:
36 + 12x + x2 = 162 + 36

Combine like terms: 162 + 36 = 198
36 + 12x + x2 = 198

Factor a perfect square on the left side:
(x + 6)(x + 6) = 198

Calculate the square root of the right side: 14.071247279

Break this problem into two subproblems by setting 
(x + 6) equal to 14.071247279 and -14.071247279.

Subproblem 1

x + 6 = 14.071247279 Simplifying x + 6 = 14.071247279 Reorder the terms: 6 + x = 14.071247279 Solving 6 + x = 14.071247279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 14.071247279 + -6 Combine like terms: 6 + -6 = 0 0 + x = 14.071247279 + -6 x = 14.071247279 + -6 Combine like terms: 14.071247279 + -6 = 8.071247279 x = 8.071247279 Simplifying x = 8.071247279

Subproblem 2

x + 6 = -14.071247279 Simplifying x + 6 = -14.071247279 Reorder the terms: 6 + x = -14.071247279 Solving 6 + x = -14.071247279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -14.071247279 + -6 Combine like terms: 6 + -6 = 0 0 + x = -14.071247279 + -6 x = -14.071247279 + -6 Combine like terms: -14.071247279 + -6 = -20.071247279 x = -20.071247279 Simplifying x = -20.071247279

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.071247279, -20.071247279}

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