x^2+18x-126=0

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Solution for x^2+18x-126=0 equation:


Simplifying
x2 + 18x + -126 = 0

Reorder the terms:
-126 + 18x + x2 = 0

Solving
-126 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '126' to each side of the equation.
-126 + 18x + 126 + x2 = 0 + 126

Reorder the terms:
-126 + 126 + 18x + x2 = 0 + 126

Combine like terms: -126 + 126 = 0
0 + 18x + x2 = 0 + 126
18x + x2 = 0 + 126

Combine like terms: 0 + 126 = 126
18x + x2 = 126

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = 126 + 81

Reorder the terms:
81 + 18x + x2 = 126 + 81

Combine like terms: 126 + 81 = 207
81 + 18x + x2 = 207

Factor a perfect square on the left side:
(x + 9)(x + 9) = 207

Calculate the square root of the right side: 14.38749457

Break this problem into two subproblems by setting 
(x + 9) equal to 14.38749457 and -14.38749457.

Subproblem 1

x + 9 = 14.38749457 Simplifying x + 9 = 14.38749457 Reorder the terms: 9 + x = 14.38749457 Solving 9 + x = 14.38749457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 14.38749457 + -9 Combine like terms: 9 + -9 = 0 0 + x = 14.38749457 + -9 x = 14.38749457 + -9 Combine like terms: 14.38749457 + -9 = 5.38749457 x = 5.38749457 Simplifying x = 5.38749457

Subproblem 2

x + 9 = -14.38749457 Simplifying x + 9 = -14.38749457 Reorder the terms: 9 + x = -14.38749457 Solving 9 + x = -14.38749457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -14.38749457 + -9 Combine like terms: 9 + -9 = 0 0 + x = -14.38749457 + -9 x = -14.38749457 + -9 Combine like terms: -14.38749457 + -9 = -23.38749457 x = -23.38749457 Simplifying x = -23.38749457

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.38749457, -23.38749457}

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