x^2-3x-63=0

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Solution for x^2-3x-63=0 equation: 


Simplifying
x2 + -3x + -63 = 0

Reorder the terms:
-63 + -3x + x2 = 0

Solving
-63 + -3x + 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 + -3x + 63 + x2 = 0 + 63

Reorder the terms:
-63 + 63 + -3x + x2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + -3x + x2 = 0 + 63
-3x + x2 = 0 + 63

Combine like terms: 0 + 63 = 63
-3x + x2 = 63

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 63 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 63 + 2.25

Combine like terms: 63 + 2.25 = 65.25
2.25 + -3x + x2 = 65.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(x + -1.5) equal to 8.077747211 and -8.077747211.


Subproblem 1
x + -1.5 = 8.077747211

Simplifying
x + -1.5 = 8.077747211

Reorder the terms:
-1.5 + x = 8.077747211

Solving
-1.5 + x = 8.077747211

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 8.077747211 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 8.077747211 + 1.5
x = 8.077747211 + 1.5

Combine like terms: 8.077747211 + 1.5 = 9.577747211
x = 9.577747211

Simplifying
x = 9.577747211


Subproblem 2
x + -1.5 = -8.077747211

Simplifying
x + -1.5 = -8.077747211

Reorder the terms:
-1.5 + x = -8.077747211

Solving
-1.5 + x = -8.077747211

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -8.077747211 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -8.077747211 + 1.5
x = -8.077747211 + 1.5

Combine like terms: -8.077747211 + 1.5 = -6.577747211
x = -6.577747211

Simplifying
x = -6.577747211


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.577747211, -6.577747211}

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