x^2-7x-12.25=16.25

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Solution for x^2-7x-12.25=16.25 equation: 


Simplifying
x2 + -7x + -12.25 = 16.25

Reorder the terms:
-12.25 + -7x + x2 = 16.25

Solving
-12.25 + -7x + x2 = 16.25

Solving for variable 'x'.

Reorder the terms:
-12.25 + -16.25 + -7x + x2 = 16.25 + -16.25

Combine like terms: -12.25 + -16.25 = -28.5
-28.5 + -7x + x2 = 16.25 + -16.25

Combine like terms: 16.25 + -16.25 = 0.00
-28.5 + -7x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '28.5' to each side of the equation.
-28.5 + -7x + 28.5 + x2 = 0.00 + 28.5

Reorder the terms:
-28.5 + 28.5 + -7x + x2 = 0.00 + 28.5

Combine like terms: -28.5 + 28.5 = 0.0
0.0 + -7x + x2 = 0.00 + 28.5
-7x + x2 = 0.00 + 28.5

Combine like terms: 0.00 + 28.5 = 28.5
-7x + x2 = 28.5

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 28.5 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 28.5 + 12.25

Combine like terms: 28.5 + 12.25 = 40.75
12.25 + -7x + x2 = 40.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 40.75

Calculate the square root of the right side: 6.383572667

Break this problem into two subproblems by setting 
(x + -3.5) equal to 6.383572667 and -6.383572667.


Subproblem 1
x + -3.5 = 6.383572667

Simplifying
x + -3.5 = 6.383572667

Reorder the terms:
-3.5 + x = 6.383572667

Solving
-3.5 + x = 6.383572667

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 6.383572667 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 6.383572667 + 3.5
x = 6.383572667 + 3.5

Combine like terms: 6.383572667 + 3.5 = 9.883572667
x = 9.883572667

Simplifying
x = 9.883572667


Subproblem 2
x + -3.5 = -6.383572667

Simplifying
x + -3.5 = -6.383572667

Reorder the terms:
-3.5 + x = -6.383572667

Solving
-3.5 + x = -6.383572667

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -6.383572667 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -6.383572667 + 3.5
x = -6.383572667 + 3.5

Combine like terms: -6.383572667 + 3.5 = -2.883572667
x = -2.883572667

Simplifying
x = -2.883572667


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.883572667, -2.883572667}

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