x^2-26x-165=0

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Solution for x^2-26x-165=0 equation:


Simplifying
x2 + -26x + -165 = 0

Reorder the terms:
-165 + -26x + x2 = 0

Solving
-165 + -26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '165' to each side of the equation.
-165 + -26x + 165 + x2 = 0 + 165

Reorder the terms:
-165 + 165 + -26x + x2 = 0 + 165

Combine like terms: -165 + 165 = 0
0 + -26x + x2 = 0 + 165
-26x + x2 = 0 + 165

Combine like terms: 0 + 165 = 165
-26x + x2 = 165

The x term is -26x.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26x + 169 + x2 = 165 + 169

Reorder the terms:
169 + -26x + x2 = 165 + 169

Combine like terms: 165 + 169 = 334
169 + -26x + x2 = 334

Factor a perfect square on the left side:
(x + -13)(x + -13) = 334

Calculate the square root of the right side: 18.275666882

Break this problem into two subproblems by setting 
(x + -13) equal to 18.275666882 and -18.275666882.

Subproblem 1

x + -13 = 18.275666882 Simplifying x + -13 = 18.275666882 Reorder the terms: -13 + x = 18.275666882 Solving -13 + x = 18.275666882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 18.275666882 + 13 Combine like terms: -13 + 13 = 0 0 + x = 18.275666882 + 13 x = 18.275666882 + 13 Combine like terms: 18.275666882 + 13 = 31.275666882 x = 31.275666882 Simplifying x = 31.275666882

Subproblem 2

x + -13 = -18.275666882 Simplifying x + -13 = -18.275666882 Reorder the terms: -13 + x = -18.275666882 Solving -13 + x = -18.275666882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -18.275666882 + 13 Combine like terms: -13 + 13 = 0 0 + x = -18.275666882 + 13 x = -18.275666882 + 13 Combine like terms: -18.275666882 + 13 = -5.275666882 x = -5.275666882 Simplifying x = -5.275666882

Solution

The solution to the problem is based on the solutions from the subproblems. x = {31.275666882, -5.275666882}

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