x^2-18x-25=96

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Solution for x^2-18x-25=96 equation:


Simplifying
x2 + -18x + -25 = 96

Reorder the terms:
-25 + -18x + x2 = 96

Solving
-25 + -18x + x2 = 96

Solving for variable 'x'.

Reorder the terms:
-25 + -96 + -18x + x2 = 96 + -96

Combine like terms: -25 + -96 = -121
-121 + -18x + x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-121 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '121' to each side of the equation.
-121 + -18x + 121 + x2 = 0 + 121

Reorder the terms:
-121 + 121 + -18x + x2 = 0 + 121

Combine like terms: -121 + 121 = 0
0 + -18x + x2 = 0 + 121
-18x + x2 = 0 + 121

Combine like terms: 0 + 121 = 121
-18x + x2 = 121

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 = 121 + 81

Reorder the terms:
81 + -18x + x2 = 121 + 81

Combine like terms: 121 + 81 = 202
81 + -18x + x2 = 202

Factor a perfect square on the left side:
(x + -9)(x + -9) = 202

Calculate the square root of the right side: 14.212670404

Break this problem into two subproblems by setting 
(x + -9) equal to 14.212670404 and -14.212670404.

Subproblem 1

x + -9 = 14.212670404 Simplifying x + -9 = 14.212670404 Reorder the terms: -9 + x = 14.212670404 Solving -9 + x = 14.212670404 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 = 14.212670404 + 9 Combine like terms: -9 + 9 = 0 0 + x = 14.212670404 + 9 x = 14.212670404 + 9 Combine like terms: 14.212670404 + 9 = 23.212670404 x = 23.212670404 Simplifying x = 23.212670404

Subproblem 2

x + -9 = -14.212670404 Simplifying x + -9 = -14.212670404 Reorder the terms: -9 + x = -14.212670404 Solving -9 + x = -14.212670404 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 = -14.212670404 + 9 Combine like terms: -9 + 9 = 0 0 + x = -14.212670404 + 9 x = -14.212670404 + 9 Combine like terms: -14.212670404 + 9 = -5.212670404 x = -5.212670404 Simplifying x = -5.212670404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.212670404, -5.212670404}

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