x^2-63x-984=0

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Solution for x^2-63x-984=0 equation: 


Simplifying
x2 + -63x + -984 = 0

Reorder the terms:
-984 + -63x + x2 = 0

Solving
-984 + -63x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '984' to each side of the equation.
-984 + -63x + 984 + x2 = 0 + 984

Reorder the terms:
-984 + 984 + -63x + x2 = 0 + 984

Combine like terms: -984 + 984 = 0
0 + -63x + x2 = 0 + 984
-63x + x2 = 0 + 984

Combine like terms: 0 + 984 = 984
-63x + x2 = 984

The x term is -63x.  Take half its coefficient (-31.5).
Square it (992.25) and add it to both sides.

Add '992.25' to each side of the equation.
-63x + 992.25 + x2 = 984 + 992.25

Reorder the terms:
992.25 + -63x + x2 = 984 + 992.25

Combine like terms: 984 + 992.25 = 1976.25
992.25 + -63x + x2 = 1976.25

Factor a perfect square on the left side:
(x + -31.5)(x + -31.5) = 1976.25

Calculate the square root of the right side: 44.455033461

Break this problem into two subproblems by setting 
(x + -31.5) equal to 44.455033461 and -44.455033461.


Subproblem 1
x + -31.5 = 44.455033461

Simplifying
x + -31.5 = 44.455033461

Reorder the terms:
-31.5 + x = 44.455033461

Solving
-31.5 + x = 44.455033461

Solving for variable 'x'.

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

Add '31.5' to each side of the equation.
-31.5 + 31.5 + x = 44.455033461 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + x = 44.455033461 + 31.5
x = 44.455033461 + 31.5

Combine like terms: 44.455033461 + 31.5 = 75.955033461
x = 75.955033461

Simplifying
x = 75.955033461


Subproblem 2
x + -31.5 = -44.455033461

Simplifying
x + -31.5 = -44.455033461

Reorder the terms:
-31.5 + x = -44.455033461

Solving
-31.5 + x = -44.455033461

Solving for variable 'x'.

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

Add '31.5' to each side of the equation.
-31.5 + 31.5 + x = -44.455033461 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + x = -44.455033461 + 31.5
x = -44.455033461 + 31.5

Combine like terms: -44.455033461 + 31.5 = -12.955033461
x = -12.955033461

Simplifying
x = -12.955033461


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {75.955033461, -12.955033461}

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