(2x+8)(x-3)=154

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Solution for (2x+8)(x-3)=154 equation: 


Simplifying
(2x + 8)(x + -3) = 154

Reorder the terms:
(8 + 2x)(x + -3) = 154

Reorder the terms:
(8 + 2x)(-3 + x) = 154

Multiply (8 + 2x) * (-3 + x)
(8(-3 + x) + 2x * (-3 + x)) = 154
((-3 * 8 + x * 8) + 2x * (-3 + x)) = 154
((-24 + 8x) + 2x * (-3 + x)) = 154
(-24 + 8x + (-3 * 2x + x * 2x)) = 154
(-24 + 8x + (-6x + 2x2)) = 154

Combine like terms: 8x + -6x = 2x
(-24 + 2x + 2x2) = 154

Solving
-24 + 2x + 2x2 = 154

Solving for variable 'x'.

Reorder the terms:
-24 + -154 + 2x + 2x2 = 154 + -154

Combine like terms: -24 + -154 = -178
-178 + 2x + 2x2 = 154 + -154

Combine like terms: 154 + -154 = 0
-178 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-89 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-89 + x + x2)' equal to zero and attempt to solve:

Simplifying
-89 + x + x2 = 0

Solving
-89 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '89' to each side of the equation.
-89 + x + 89 + x2 = 0 + 89

Reorder the terms:
-89 + 89 + x + x2 = 0 + 89

Combine like terms: -89 + 89 = 0
0 + x + x2 = 0 + 89
x + x2 = 0 + 89

Combine like terms: 0 + 89 = 89
x + x2 = 89

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 89 + 0.25

Reorder the terms:
0.25 + x + x2 = 89 + 0.25

Combine like terms: 89 + 0.25 = 89.25
0.25 + x + x2 = 89.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 89.25

Calculate the square root of the right side: 9.447221814

Break this problem into two subproblems by setting 
(x + 0.5) equal to 9.447221814 and -9.447221814.


Subproblem 1
x + 0.5 = 9.447221814

Simplifying
x + 0.5 = 9.447221814

Reorder the terms:
0.5 + x = 9.447221814

Solving
0.5 + x = 9.447221814

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 9.447221814 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 9.447221814 + -0.5
x = 9.447221814 + -0.5

Combine like terms: 9.447221814 + -0.5 = 8.947221814
x = 8.947221814

Simplifying
x = 8.947221814


Subproblem 2
x + 0.5 = -9.447221814

Simplifying
x + 0.5 = -9.447221814

Reorder the terms:
0.5 + x = -9.447221814

Solving
0.5 + x = -9.447221814

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -9.447221814 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -9.447221814 + -0.5
x = -9.447221814 + -0.5

Combine like terms: -9.447221814 + -0.5 = -9.947221814
x = -9.947221814

Simplifying
x = -9.947221814


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.947221814, -9.947221814}
Solution
x = {8.947221814, -9.947221814}

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