x^2+5x-64=0

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Solution for x^2+5x-64=0 equation:


Simplifying
x2 + 5x + -64 = 0

Reorder the terms:
-64 + 5x + x2 = 0

Solving
-64 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 5x + 64 + x2 = 0 + 64

Reorder the terms:
-64 + 64 + 5x + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 5x + x2 = 0 + 64
5x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
5x + x2 = 64

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 64 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 64 + 6.25

Combine like terms: 64 + 6.25 = 70.25
6.25 + 5x + x2 = 70.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 70.25

Calculate the square root of the right side: 8.381527307

Break this problem into two subproblems by setting 
(x + 2.5) equal to 8.381527307 and -8.381527307.


Subproblem 1
x + 2.5 = 8.381527307

Simplifying
x + 2.5 = 8.381527307

Reorder the terms:
2.5 + x = 8.381527307

Solving
2.5 + x = 8.381527307

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 8.381527307 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 8.381527307 + -2.5
x = 8.381527307 + -2.5

Combine like terms: 8.381527307 + -2.5 = 5.881527307
x = 5.881527307

Simplifying
x = 5.881527307


Subproblem 2
x + 2.5 = -8.381527307

Simplifying
x + 2.5 = -8.381527307

Reorder the terms:
2.5 + x = -8.381527307

Solving
2.5 + x = -8.381527307

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -8.381527307 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -8.381527307 + -2.5
x = -8.381527307 + -2.5

Combine like terms: -8.381527307 + -2.5 = -10.881527307
x = -10.881527307

Simplifying
x = -10.881527307


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.881527307, -10.881527307}

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