-.5x^2+9x-8.75=0

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Solution for -.5x^2+9x-8.75=0 equation: 


Simplifying
-0.5x2 + 9x + -8.75 = 0

Reorder the terms:
-8.75 + 9x + -0.5x2 = 0

Solving
-8.75 + 9x + -0.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
17.5 + -18x + x2 = 0

Move the constant term to the right:

Add '-17.5' to each side of the equation.
17.5 + -18x + -17.5 + x2 = 0 + -17.5

Reorder the terms:
17.5 + -17.5 + -18x + x2 = 0 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + -18x + x2 = 0 + -17.5
-18x + x2 = 0 + -17.5

Combine like terms: 0 + -17.5 = -17.5
-18x + x2 = -17.5

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -17.5 + 81

Reorder the terms:
81 + -18x + x2 = -17.5 + 81

Combine like terms: -17.5 + 81 = 63.5
81 + -18x + x2 = 63.5

Factor a perfect square on the left side:
(x + -9)(x + -9) = 63.5

Calculate the square root of the right side: 7.968688725

Break this problem into two subproblems by setting 
(x + -9) equal to 7.968688725 and -7.968688725.


Subproblem 1
x + -9 = 7.968688725

Simplifying
x + -9 = 7.968688725

Reorder the terms:
-9 + x = 7.968688725

Solving
-9 + x = 7.968688725

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 7.968688725 + 9

Combine like terms: -9 + 9 = 0
0 + x = 7.968688725 + 9
x = 7.968688725 + 9

Combine like terms: 7.968688725 + 9 = 16.968688725
x = 16.968688725

Simplifying
x = 16.968688725


Subproblem 2
x + -9 = -7.968688725

Simplifying
x + -9 = -7.968688725

Reorder the terms:
-9 + x = -7.968688725

Solving
-9 + x = -7.968688725

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -7.968688725 + 9

Combine like terms: -9 + 9 = 0
0 + x = -7.968688725 + 9
x = -7.968688725 + 9

Combine like terms: -7.968688725 + 9 = 1.031311275
x = 1.031311275

Simplifying
x = 1.031311275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.968688725, 1.031311275}

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