2x-7=8x(x-3)

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Solution for 2x-7=8x(x-3) equation: 


Simplifying
2x + -7 = 8x(x + -3)

Reorder the terms:
-7 + 2x = 8x(x + -3)

Reorder the terms:
-7 + 2x = 8x(-3 + x)
-7 + 2x = (-3 * 8x + x * 8x)
-7 + 2x = (-24x + 8x2)

Solving
-7 + 2x = -24x + 8x2

Solving for variable 'x'.

Combine like terms: 2x + 24x = 26x
-7 + 26x + -8x2 = -24x + 8x2 + 24x + -8x2

Reorder the terms:
-7 + 26x + -8x2 = -24x + 24x + 8x2 + -8x2

Combine like terms: -24x + 24x = 0
-7 + 26x + -8x2 = 0 + 8x2 + -8x2
-7 + 26x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-7 + 26x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.875 + -3.25x + x2 = 0

Move the constant term to the right:

Add '-0.875' to each side of the equation.
0.875 + -3.25x + -0.875 + x2 = 0 + -0.875

Reorder the terms:
0.875 + -0.875 + -3.25x + x2 = 0 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + -3.25x + x2 = 0 + -0.875
-3.25x + x2 = 0 + -0.875

Combine like terms: 0 + -0.875 = -0.875
-3.25x + x2 = -0.875

The x term is -3.25x.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25x + 2.640625 + x2 = -0.875 + 2.640625

Reorder the terms:
2.640625 + -3.25x + x2 = -0.875 + 2.640625

Combine like terms: -0.875 + 2.640625 = 1.765625
2.640625 + -3.25x + x2 = 1.765625

Factor a perfect square on the left side:
(x + -1.625)(x + -1.625) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(x + -1.625) equal to 1.328768227 and -1.328768227.


Subproblem 1
x + -1.625 = 1.328768227

Simplifying
x + -1.625 = 1.328768227

Reorder the terms:
-1.625 + x = 1.328768227

Solving
-1.625 + x = 1.328768227

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = 1.328768227 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = 1.328768227 + 1.625
x = 1.328768227 + 1.625

Combine like terms: 1.328768227 + 1.625 = 2.953768227
x = 2.953768227

Simplifying
x = 2.953768227


Subproblem 2
x + -1.625 = -1.328768227

Simplifying
x + -1.625 = -1.328768227

Reorder the terms:
-1.625 + x = -1.328768227

Solving
-1.625 + x = -1.328768227

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = -1.328768227 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = -1.328768227 + 1.625
x = -1.328768227 + 1.625

Combine like terms: -1.328768227 + 1.625 = 0.296231773
x = 0.296231773

Simplifying
x = 0.296231773


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.953768227, 0.296231773}

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