0.75x^2-9.5x-7.25=0

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Solution for 0.75x^2-9.5x-7.25=0 equation: 


Simplifying
0.75x2 + -9.5x + -7.25 = 0

Reorder the terms:
-7.25 + -9.5x + 0.75x2 = 0

Solving
-7.25 + -9.5x + 0.75x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.75 the coefficient of the squared term: 

Divide each side by '0.75'.
-9.666666667 + -12.66666667x + x2 = 0

Move the constant term to the right:

Add '9.666666667' to each side of the equation.
-9.666666667 + -12.66666667x + 9.666666667 + x2 = 0 + 9.666666667

Reorder the terms:
-9.666666667 + 9.666666667 + -12.66666667x + x2 = 0 + 9.666666667

Combine like terms: -9.666666667 + 9.666666667 = 0.000000000
0.000000000 + -12.66666667x + x2 = 0 + 9.666666667
-12.66666667x + x2 = 0 + 9.666666667

Combine like terms: 0 + 9.666666667 = 9.666666667
-12.66666667x + x2 = 9.666666667

The x term is -12.66666667x.  Take half its coefficient (-6.333333335).
Square it (40.11111113) and add it to both sides.

Add '40.11111113' to each side of the equation.
-12.66666667x + 40.11111113 + x2 = 9.666666667 + 40.11111113

Reorder the terms:
40.11111113 + -12.66666667x + x2 = 9.666666667 + 40.11111113

Combine like terms: 9.666666667 + 40.11111113 = 49.777777797
40.11111113 + -12.66666667x + x2 = 49.777777797

Factor a perfect square on the left side:
(x + -6.333333335)(x + -6.333333335) = 49.777777797

Calculate the square root of the right side: 7.055336831

Break this problem into two subproblems by setting 
(x + -6.333333335) equal to 7.055336831 and -7.055336831.


Subproblem 1
x + -6.333333335 = 7.055336831

Simplifying
x + -6.333333335 = 7.055336831

Reorder the terms:
-6.333333335 + x = 7.055336831

Solving
-6.333333335 + x = 7.055336831

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = 7.055336831 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = 7.055336831 + 6.333333335
x = 7.055336831 + 6.333333335

Combine like terms: 7.055336831 + 6.333333335 = 13.388670166
x = 13.388670166

Simplifying
x = 13.388670166


Subproblem 2
x + -6.333333335 = -7.055336831

Simplifying
x + -6.333333335 = -7.055336831

Reorder the terms:
-6.333333335 + x = -7.055336831

Solving
-6.333333335 + x = -7.055336831

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = -7.055336831 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = -7.055336831 + 6.333333335
x = -7.055336831 + 6.333333335

Combine like terms: -7.055336831 + 6.333333335 = -0.722003496
x = -0.722003496

Simplifying
x = -0.722003496


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.388670166, -0.722003496}

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