8x+8+32x=8x^2+8x

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Solution for 8x+8+32x=8x^2+8x equation: 


Simplifying
8x + 8 + 32x = 8x2 + 8x

Reorder the terms:
8 + 8x + 32x = 8x2 + 8x

Combine like terms: 8x + 32x = 40x
8 + 40x = 8x2 + 8x

Reorder the terms:
8 + 40x = 8x + 8x2

Solving
8 + 40x = 8x + 8x2

Solving for variable 'x'.

Combine like terms: 40x + -8x = 32x
8 + 32x + -8x2 = 8x + 8x2 + -8x + -8x2

Reorder the terms:
8 + 32x + -8x2 = 8x + -8x + 8x2 + -8x2

Combine like terms: 8x + -8x = 0
8 + 32x + -8x2 = 0 + 8x2 + -8x2
8 + 32x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
8 + 32x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + 4x + -1x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(1 + 4x + -1x2)' equal to zero and attempt to solve:

Simplifying
1 + 4x + -1x2 = 0

Solving
1 + 4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -4x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x + x2 = 0 + 1
-4x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4x + x2 = 1

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1 + 4

Reorder the terms:
4 + -4x + x2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + -4x + x2 = 5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -2) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + -2 = 2.236067978

Simplifying
x + -2 = 2.236067978

Reorder the terms:
-2 + x = 2.236067978

Solving
-2 + x = 2.236067978

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.236067978 + 2
x = 2.236067978 + 2

Combine like terms: 2.236067978 + 2 = 4.236067978
x = 4.236067978

Simplifying
x = 4.236067978


Subproblem 2
x + -2 = -2.236067978

Simplifying
x + -2 = -2.236067978

Reorder the terms:
-2 + x = -2.236067978

Solving
-2 + x = -2.236067978

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.236067978 + 2
x = -2.236067978 + 2

Combine like terms: -2.236067978 + 2 = -0.236067978
x = -0.236067978

Simplifying
x = -0.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.236067978, -0.236067978}
Solution
x = {4.236067978, -0.236067978}

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