x^2-26x=-145

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Solution for x^2-26x=-145 equation:


Simplifying
x2 + -26x = -145

Reorder the terms:
-26x + x2 = -145

Solving
-26x + x2 = -145

Solving for variable 'x'.

Reorder the terms:
145 + -26x + x2 = -145 + 145

Combine like terms: -145 + 145 = 0
145 + -26x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-145' to each side of the equation.
145 + -26x + -145 + x2 = 0 + -145

Reorder the terms:
145 + -145 + -26x + x2 = 0 + -145

Combine like terms: 145 + -145 = 0
0 + -26x + x2 = 0 + -145
-26x + x2 = 0 + -145

Combine like terms: 0 + -145 = -145
-26x + x2 = -145

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 = -145 + 169

Reorder the terms:
169 + -26x + x2 = -145 + 169

Combine like terms: -145 + 169 = 24
169 + -26x + x2 = 24

Factor a perfect square on the left side:
(x + -13)(x + -13) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -13) equal to 4.898979486 and -4.898979486.

Subproblem 1

x + -13 = 4.898979486 Simplifying x + -13 = 4.898979486 Reorder the terms: -13 + x = 4.898979486 Solving -13 + x = 4.898979486 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 = 4.898979486 + 13 Combine like terms: -13 + 13 = 0 0 + x = 4.898979486 + 13 x = 4.898979486 + 13 Combine like terms: 4.898979486 + 13 = 17.898979486 x = 17.898979486 Simplifying x = 17.898979486

Subproblem 2

x + -13 = -4.898979486 Simplifying x + -13 = -4.898979486 Reorder the terms: -13 + x = -4.898979486 Solving -13 + x = -4.898979486 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 = -4.898979486 + 13 Combine like terms: -13 + 13 = 0 0 + x = -4.898979486 + 13 x = -4.898979486 + 13 Combine like terms: -4.898979486 + 13 = 8.101020514 x = 8.101020514 Simplifying x = 8.101020514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.898979486, 8.101020514}

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