x^2-53x+114=0

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Solution for x^2-53x+114=0 equation: 


Simplifying
x2 + -53x + 114 = 0

Reorder the terms:
114 + -53x + x2 = 0

Solving
114 + -53x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-114' to each side of the equation.
114 + -53x + -114 + x2 = 0 + -114

Reorder the terms:
114 + -114 + -53x + x2 = 0 + -114

Combine like terms: 114 + -114 = 0
0 + -53x + x2 = 0 + -114
-53x + x2 = 0 + -114

Combine like terms: 0 + -114 = -114
-53x + x2 = -114

The x term is -53x.  Take half its coefficient (-26.5).
Square it (702.25) and add it to both sides.

Add '702.25' to each side of the equation.
-53x + 702.25 + x2 = -114 + 702.25

Reorder the terms:
702.25 + -53x + x2 = -114 + 702.25

Combine like terms: -114 + 702.25 = 588.25
702.25 + -53x + x2 = 588.25

Factor a perfect square on the left side:
(x + -26.5)(x + -26.5) = 588.25

Calculate the square root of the right side: 24.253865671

Break this problem into two subproblems by setting 
(x + -26.5) equal to 24.253865671 and -24.253865671.


Subproblem 1
x + -26.5 = 24.253865671

Simplifying
x + -26.5 = 24.253865671

Reorder the terms:
-26.5 + x = 24.253865671

Solving
-26.5 + x = 24.253865671

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '26.5' to each side of the equation.
-26.5 + 26.5 + x = 24.253865671 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = 24.253865671 + 26.5
x = 24.253865671 + 26.5

Combine like terms: 24.253865671 + 26.5 = 50.753865671
x = 50.753865671

Simplifying
x = 50.753865671


Subproblem 2
x + -26.5 = -24.253865671

Simplifying
x + -26.5 = -24.253865671

Reorder the terms:
-26.5 + x = -24.253865671

Solving
-26.5 + x = -24.253865671

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '26.5' to each side of the equation.
-26.5 + 26.5 + x = -24.253865671 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = -24.253865671 + 26.5
x = -24.253865671 + 26.5

Combine like terms: -24.253865671 + 26.5 = 2.246134329
x = 2.246134329

Simplifying
x = 2.246134329


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.753865671, 2.246134329}

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