x^2+53x-63=0

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Solution for x^2+53x-63=0 equation: 


Simplifying
x2 + 53x + -63 = 0

Reorder the terms:
-63 + 53x + x2 = 0

Solving
-63 + 53x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '63' to each side of the equation.
-63 + 53x + 63 + x2 = 0 + 63

Reorder the terms:
-63 + 63 + 53x + x2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + 53x + x2 = 0 + 63
53x + x2 = 0 + 63

Combine like terms: 0 + 63 = 63
53x + x2 = 63

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 = 63 + 702.25

Reorder the terms:
702.25 + 53x + x2 = 63 + 702.25

Combine like terms: 63 + 702.25 = 765.25
702.25 + 53x + x2 = 765.25

Factor a perfect square on the left side:
(x + 26.5)(x + 26.5) = 765.25

Calculate the square root of the right side: 27.663152387

Break this problem into two subproblems by setting 
(x + 26.5) equal to 27.663152387 and -27.663152387.


Subproblem 1
x + 26.5 = 27.663152387

Simplifying
x + 26.5 = 27.663152387

Reorder the terms:
26.5 + x = 27.663152387

Solving
26.5 + x = 27.663152387

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 = 27.663152387 + -26.5

Combine like terms: 26.5 + -26.5 = 0.0
0.0 + x = 27.663152387 + -26.5
x = 27.663152387 + -26.5

Combine like terms: 27.663152387 + -26.5 = 1.163152387
x = 1.163152387

Simplifying
x = 1.163152387


Subproblem 2
x + 26.5 = -27.663152387

Simplifying
x + 26.5 = -27.663152387

Reorder the terms:
26.5 + x = -27.663152387

Solving
26.5 + x = -27.663152387

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 = -27.663152387 + -26.5

Combine like terms: 26.5 + -26.5 = 0.0
0.0 + x = -27.663152387 + -26.5
x = -27.663152387 + -26.5

Combine like terms: -27.663152387 + -26.5 = -54.163152387
x = -54.163152387

Simplifying
x = -54.163152387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.163152387, -54.163152387}

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