x^2+12x-23=180

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Solution for x^2+12x-23=180 equation:


Simplifying
x2 + 12x + -23 = 180

Reorder the terms:
-23 + 12x + x2 = 180

Solving
-23 + 12x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-23 + -180 + 12x + x2 = 180 + -180

Combine like terms: -23 + -180 = -203
-203 + 12x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-203 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '203' to each side of the equation.
-203 + 12x + 203 + x2 = 0 + 203

Reorder the terms:
-203 + 203 + 12x + x2 = 0 + 203

Combine like terms: -203 + 203 = 0
0 + 12x + x2 = 0 + 203
12x + x2 = 0 + 203

Combine like terms: 0 + 203 = 203
12x + x2 = 203

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 = 203 + 36

Reorder the terms:
36 + 12x + x2 = 203 + 36

Combine like terms: 203 + 36 = 239
36 + 12x + x2 = 239

Factor a perfect square on the left side:
(x + 6)(x + 6) = 239

Calculate the square root of the right side: 15.459624834

Break this problem into two subproblems by setting 
(x + 6) equal to 15.459624834 and -15.459624834.

Subproblem 1

x + 6 = 15.459624834 Simplifying x + 6 = 15.459624834 Reorder the terms: 6 + x = 15.459624834 Solving 6 + x = 15.459624834 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 = 15.459624834 + -6 Combine like terms: 6 + -6 = 0 0 + x = 15.459624834 + -6 x = 15.459624834 + -6 Combine like terms: 15.459624834 + -6 = 9.459624834 x = 9.459624834 Simplifying x = 9.459624834

Subproblem 2

x + 6 = -15.459624834 Simplifying x + 6 = -15.459624834 Reorder the terms: 6 + x = -15.459624834 Solving 6 + x = -15.459624834 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 = -15.459624834 + -6 Combine like terms: 6 + -6 = 0 0 + x = -15.459624834 + -6 x = -15.459624834 + -6 Combine like terms: -15.459624834 + -6 = -21.459624834 x = -21.459624834 Simplifying x = -21.459624834

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.459624834, -21.459624834}

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