9x+8-2x(x-5)+7=

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Solution for 9x+8-2x(x-5)+7= equation: 


Simplifying
9x + 8 + -2x(x + -5) + 7 = 0

Reorder the terms:
9x + 8 + -2x(-5 + x) + 7 = 0
9x + 8 + (-5 * -2x + x * -2x) + 7 = 0
9x + 8 + (10x + -2x2) + 7 = 0

Reorder the terms:
8 + 7 + 9x + 10x + -2x2 = 0

Combine like terms: 8 + 7 = 15
15 + 9x + 10x + -2x2 = 0

Combine like terms: 9x + 10x = 19x
15 + 19x + -2x2 = 0

Solving
15 + 19x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-7.5 + -9.5x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -9.5x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -9.5x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -9.5x + x2 = 0 + 7.5
-9.5x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-9.5x + x2 = 7.5

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = 7.5 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = 7.5 + 22.5625

Combine like terms: 7.5 + 22.5625 = 30.0625
22.5625 + -9.5x + x2 = 30.0625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 30.0625

Calculate the square root of the right side: 5.48292805

Break this problem into two subproblems by setting 
(x + -4.75) equal to 5.48292805 and -5.48292805.


Subproblem 1
x + -4.75 = 5.48292805

Simplifying
x + -4.75 = 5.48292805

Reorder the terms:
-4.75 + x = 5.48292805

Solving
-4.75 + x = 5.48292805

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = 5.48292805 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = 5.48292805 + 4.75
x = 5.48292805 + 4.75

Combine like terms: 5.48292805 + 4.75 = 10.23292805
x = 10.23292805

Simplifying
x = 10.23292805


Subproblem 2
x + -4.75 = -5.48292805

Simplifying
x + -4.75 = -5.48292805

Reorder the terms:
-4.75 + x = -5.48292805

Solving
-4.75 + x = -5.48292805

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = -5.48292805 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = -5.48292805 + 4.75
x = -5.48292805 + 4.75

Combine like terms: -5.48292805 + 4.75 = -0.73292805
x = -0.73292805

Simplifying
x = -0.73292805


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.23292805, -0.73292805}

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