x^2+18x-124=0

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Solution for x^2+18x-124=0 equation:


Simplifying
x2 + 18x + -124 = 0

Reorder the terms:
-124 + 18x + x2 = 0

Solving
-124 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '124' to each side of the equation.
-124 + 18x + 124 + x2 = 0 + 124

Reorder the terms:
-124 + 124 + 18x + x2 = 0 + 124

Combine like terms: -124 + 124 = 0
0 + 18x + x2 = 0 + 124
18x + x2 = 0 + 124

Combine like terms: 0 + 124 = 124
18x + x2 = 124

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 = 124 + 81

Reorder the terms:
81 + 18x + x2 = 124 + 81

Combine like terms: 124 + 81 = 205
81 + 18x + x2 = 205

Factor a perfect square on the left side:
(x + 9)(x + 9) = 205

Calculate the square root of the right side: 14.317821063

Break this problem into two subproblems by setting 
(x + 9) equal to 14.317821063 and -14.317821063.

Subproblem 1

x + 9 = 14.317821063 Simplifying x + 9 = 14.317821063 Reorder the terms: 9 + x = 14.317821063 Solving 9 + x = 14.317821063 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 = 14.317821063 + -9 Combine like terms: 9 + -9 = 0 0 + x = 14.317821063 + -9 x = 14.317821063 + -9 Combine like terms: 14.317821063 + -9 = 5.317821063 x = 5.317821063 Simplifying x = 5.317821063

Subproblem 2

x + 9 = -14.317821063 Simplifying x + 9 = -14.317821063 Reorder the terms: 9 + x = -14.317821063 Solving 9 + x = -14.317821063 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 = -14.317821063 + -9 Combine like terms: 9 + -9 = 0 0 + x = -14.317821063 + -9 x = -14.317821063 + -9 Combine like terms: -14.317821063 + -9 = -23.317821063 x = -23.317821063 Simplifying x = -23.317821063

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.317821063, -23.317821063}

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