x^2+53x-226=0

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Solution for x^2+53x-226=0 equation: 


Simplifying
x2 + 53x + -226 = 0

Reorder the terms:
-226 + 53x + x2 = 0

Solving
-226 + 53x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '226' to each side of the equation.
-226 + 53x + 226 + x2 = 0 + 226

Reorder the terms:
-226 + 226 + 53x + x2 = 0 + 226

Combine like terms: -226 + 226 = 0
0 + 53x + x2 = 0 + 226
53x + x2 = 0 + 226

Combine like terms: 0 + 226 = 226
53x + x2 = 226

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 = 226 + 702.25

Reorder the terms:
702.25 + 53x + x2 = 226 + 702.25

Combine like terms: 226 + 702.25 = 928.25
702.25 + 53x + x2 = 928.25

Factor a perfect square on the left side:
(x + 26.5)(x + 26.5) = 928.25

Calculate the square root of the right side: 30.467195473

Break this problem into two subproblems by setting 
(x + 26.5) equal to 30.467195473 and -30.467195473.


Subproblem 1
x + 26.5 = 30.467195473

Simplifying
x + 26.5 = 30.467195473

Reorder the terms:
26.5 + x = 30.467195473

Solving
26.5 + x = 30.467195473

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 = 30.467195473 + -26.5

Combine like terms: 26.5 + -26.5 = 0.0
0.0 + x = 30.467195473 + -26.5
x = 30.467195473 + -26.5

Combine like terms: 30.467195473 + -26.5 = 3.967195473
x = 3.967195473

Simplifying
x = 3.967195473


Subproblem 2
x + 26.5 = -30.467195473

Simplifying
x + 26.5 = -30.467195473

Reorder the terms:
26.5 + x = -30.467195473

Solving
26.5 + x = -30.467195473

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 = -30.467195473 + -26.5

Combine like terms: 26.5 + -26.5 = 0.0
0.0 + x = -30.467195473 + -26.5
x = -30.467195473 + -26.5

Combine like terms: -30.467195473 + -26.5 = -56.967195473
x = -56.967195473

Simplifying
x = -56.967195473


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.967195473, -56.967195473}

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