x^2-(9x+8)*8=3x

Solution for x^2-(9x+8)*8=3x equation:

Simplifying
x2 + -1(9x + 8) * 8 = 3x

Reorder the terms:
x2 + -1(8 + 9x) * 8 = 3x

Reorder the terms for easier multiplication:
x2 + -1 * 8(8 + 9x) = 3x

Multiply -1 * 8
x2 + -8(8 + 9x) = 3x
x2 + (8 * -8 + 9x * -8) = 3x
x2 + (-64 + -72x) = 3x

Reorder the terms:
-64 + -72x + x2 = 3x

Solving
-64 + -72x + x2 = 3x

Solving for variable 'x'.

Reorder the terms:
-64 + -72x + -3x + x2 = 3x + -3x

Combine like terms: -72x + -3x = -75x
-64 + -75x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-64 + -75x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -75x + 64 + x2 = 0 + 64

Reorder the terms:
-64 + 64 + -75x + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -75x + x2 = 0 + 64
-75x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
-75x + x2 = 64

The x term is -75x.  Take half its coefficient (-37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
-75x + 1406.25 + x2 = 64 + 1406.25

Reorder the terms:
1406.25 + -75x + x2 = 64 + 1406.25

Combine like terms: 64 + 1406.25 = 1470.25
1406.25 + -75x + x2 = 1470.25

Factor a perfect square on the left side:
(x + -37.5)(x + -37.5) = 1470.25

Calculate the square root of the right side: 38.34383914

Break this problem into two subproblems by setting 
(x + -37.5) equal to 38.34383914 and -38.34383914.

Subproblem 1
x + -37.5 = 38.34383914

Simplifying
x + -37.5 = 38.34383914

Reorder the terms:
-37.5 + x = 38.34383914

Solving
-37.5 + x = 38.34383914

Solving for variable 'x'.

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

Add '37.5' to each side of the equation.
-37.5 + 37.5 + x = 38.34383914 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + x = 38.34383914 + 37.5
x = 38.34383914 + 37.5

Combine like terms: 38.34383914 + 37.5 = 75.84383914
x = 75.84383914

Simplifying
x = 75.84383914

Subproblem 2
x + -37.5 = -38.34383914

Simplifying
x + -37.5 = -38.34383914

Reorder the terms:
-37.5 + x = -38.34383914

Solving
-37.5 + x = -38.34383914

Solving for variable 'x'.

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

Add '37.5' to each side of the equation.
-37.5 + 37.5 + x = -38.34383914 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + x = -38.34383914 + 37.5
x = -38.34383914 + 37.5

Combine like terms: -38.34383914 + 37.5 = -0.84383914
x = -0.84383914

Simplifying
x = -0.84383914

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {75.84383914, -0.84383914}