x^2-6.5*x-7.5=0

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Solution for x^2-6.5*x-7.5=0 equation: 


Simplifying
x2 + -6.5x + -7.5 = 0

Reorder the terms:
-7.5 + -6.5x + x2 = 0

Solving
-7.5 + -6.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -6.5x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -6.5x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -6.5x + x2 = 0 + 7.5
-6.5x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-6.5x + x2 = 7.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 7.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 7.5 + 10.5625

Combine like terms: 7.5 + 10.5625 = 18.0625
10.5625 + -6.5x + x2 = 18.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 18.0625

Calculate the square root of the right side: 4.25

Break this problem into two subproblems by setting 
(x + -3.25) equal to 4.25 and -4.25.


Subproblem 1
x + -3.25 = 4.25

Simplifying
x + -3.25 = 4.25

Reorder the terms:
-3.25 + x = 4.25

Solving
-3.25 + x = 4.25

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 4.25 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 4.25 + 3.25
x = 4.25 + 3.25

Combine like terms: 4.25 + 3.25 = 7.5
x = 7.5

Simplifying
x = 7.5


Subproblem 2
x + -3.25 = -4.25

Simplifying
x + -3.25 = -4.25

Reorder the terms:
-3.25 + x = -4.25

Solving
-3.25 + x = -4.25

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -4.25 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -4.25 + 3.25
x = -4.25 + 3.25

Combine like terms: -4.25 + 3.25 = -1
x = -1

Simplifying
x = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.5, -1}

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