x^2-26x+96=0

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Solution for x^2-26x+96=0 equation:


Simplifying
x2 + -26x + 96 = 0

Reorder the terms:
96 + -26x + x2 = 0

Solving
96 + -26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-96' to each side of the equation.
96 + -26x + -96 + x2 = 0 + -96

Reorder the terms:
96 + -96 + -26x + x2 = 0 + -96

Combine like terms: 96 + -96 = 0
0 + -26x + x2 = 0 + -96
-26x + x2 = 0 + -96

Combine like terms: 0 + -96 = -96
-26x + x2 = -96

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 = -96 + 169

Reorder the terms:
169 + -26x + x2 = -96 + 169

Combine like terms: -96 + 169 = 73
169 + -26x + x2 = 73

Factor a perfect square on the left side:
(x + -13)(x + -13) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(x + -13) equal to 8.544003745 and -8.544003745.

Subproblem 1

x + -13 = 8.544003745 Simplifying x + -13 = 8.544003745 Reorder the terms: -13 + x = 8.544003745 Solving -13 + x = 8.544003745 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 = 8.544003745 + 13 Combine like terms: -13 + 13 = 0 0 + x = 8.544003745 + 13 x = 8.544003745 + 13 Combine like terms: 8.544003745 + 13 = 21.544003745 x = 21.544003745 Simplifying x = 21.544003745

Subproblem 2

x + -13 = -8.544003745 Simplifying x + -13 = -8.544003745 Reorder the terms: -13 + x = -8.544003745 Solving -13 + x = -8.544003745 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 = -8.544003745 + 13 Combine like terms: -13 + 13 = 0 0 + x = -8.544003745 + 13 x = -8.544003745 + 13 Combine like terms: -8.544003745 + 13 = 4.455996255 x = 4.455996255 Simplifying x = 4.455996255

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.544003745, 4.455996255}

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