x^2-26x+156=0

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Solution for x^2-26x+156=0 equation:


Simplifying
x2 + -26x + 156 = 0

Reorder the terms:
156 + -26x + x2 = 0

Solving
156 + -26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-156' to each side of the equation.
156 + -26x + -156 + x2 = 0 + -156

Reorder the terms:
156 + -156 + -26x + x2 = 0 + -156

Combine like terms: 156 + -156 = 0
0 + -26x + x2 = 0 + -156
-26x + x2 = 0 + -156

Combine like terms: 0 + -156 = -156
-26x + x2 = -156

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 = -156 + 169

Reorder the terms:
169 + -26x + x2 = -156 + 169

Combine like terms: -156 + 169 = 13
169 + -26x + x2 = 13

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

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -13) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + -13 = 3.605551275 Simplifying x + -13 = 3.605551275 Reorder the terms: -13 + x = 3.605551275 Solving -13 + x = 3.605551275 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 = 3.605551275 + 13 Combine like terms: -13 + 13 = 0 0 + x = 3.605551275 + 13 x = 3.605551275 + 13 Combine like terms: 3.605551275 + 13 = 16.605551275 x = 16.605551275 Simplifying x = 16.605551275

Subproblem 2

x + -13 = -3.605551275 Simplifying x + -13 = -3.605551275 Reorder the terms: -13 + x = -3.605551275 Solving -13 + x = -3.605551275 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 = -3.605551275 + 13 Combine like terms: -13 + 13 = 0 0 + x = -3.605551275 + 13 x = -3.605551275 + 13 Combine like terms: -3.605551275 + 13 = 9.394448725 x = 9.394448725 Simplifying x = 9.394448725

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.605551275, 9.394448725}

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