x^2-5x-6.25=14.25

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Solution for x^2-5x-6.25=14.25 equation: 


Simplifying
x2 + -5x + -6.25 = 14.25

Reorder the terms:
-6.25 + -5x + x2 = 14.25

Solving
-6.25 + -5x + x2 = 14.25

Solving for variable 'x'.

Reorder the terms:
-6.25 + -14.25 + -5x + x2 = 14.25 + -14.25

Combine like terms: -6.25 + -14.25 = -20.5
-20.5 + -5x + x2 = 14.25 + -14.25

Combine like terms: 14.25 + -14.25 = 0.00
-20.5 + -5x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '20.5' to each side of the equation.
-20.5 + -5x + 20.5 + x2 = 0.00 + 20.5

Reorder the terms:
-20.5 + 20.5 + -5x + x2 = 0.00 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + -5x + x2 = 0.00 + 20.5
-5x + x2 = 0.00 + 20.5

Combine like terms: 0.00 + 20.5 = 20.5
-5x + x2 = 20.5

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 = 20.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 20.5 + 6.25

Combine like terms: 20.5 + 6.25 = 26.75
6.25 + -5x + x2 = 26.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 26.75

Calculate the square root of the right side: 5.172040216

Break this problem into two subproblems by setting 
(x + -2.5) equal to 5.172040216 and -5.172040216.


Subproblem 1
x + -2.5 = 5.172040216

Simplifying
x + -2.5 = 5.172040216

Reorder the terms:
-2.5 + x = 5.172040216

Solving
-2.5 + x = 5.172040216

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 = 5.172040216 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 5.172040216 + 2.5
x = 5.172040216 + 2.5

Combine like terms: 5.172040216 + 2.5 = 7.672040216
x = 7.672040216

Simplifying
x = 7.672040216


Subproblem 2
x + -2.5 = -5.172040216

Simplifying
x + -2.5 = -5.172040216

Reorder the terms:
-2.5 + x = -5.172040216

Solving
-2.5 + x = -5.172040216

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 = -5.172040216 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -5.172040216 + 2.5
x = -5.172040216 + 2.5

Combine like terms: -5.172040216 + 2.5 = -2.672040216
x = -2.672040216

Simplifying
x = -2.672040216


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.672040216, -2.672040216}

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