(5+x)(2x-2)=190

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Solution for (5+x)(2x-2)=190 equation: 


Simplifying
(5 + x)(2x + -2) = 190

Reorder the terms:
(5 + x)(-2 + 2x) = 190

Multiply (5 + x) * (-2 + 2x)
(5(-2 + 2x) + x(-2 + 2x)) = 190
((-2 * 5 + 2x * 5) + x(-2 + 2x)) = 190
((-10 + 10x) + x(-2 + 2x)) = 190
(-10 + 10x + (-2 * x + 2x * x)) = 190
(-10 + 10x + (-2x + 2x2)) = 190

Combine like terms: 10x + -2x = 8x
(-10 + 8x + 2x2) = 190

Solving
-10 + 8x + 2x2 = 190

Solving for variable 'x'.

Reorder the terms:
-10 + -190 + 8x + 2x2 = 190 + -190

Combine like terms: -10 + -190 = -200
-200 + 8x + 2x2 = 190 + -190

Combine like terms: 190 + -190 = 0
-200 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-100 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-100 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-100 + 4x + x2 = 0

Solving
-100 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 4x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 4x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 4x + x2 = 0 + 100
4x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
4x + x2 = 100

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 = 100 + 4

Reorder the terms:
4 + 4x + x2 = 100 + 4

Combine like terms: 100 + 4 = 104
4 + 4x + x2 = 104

Factor a perfect square on the left side:
(x + 2)(x + 2) = 104

Calculate the square root of the right side: 10.198039027

Break this problem into two subproblems by setting 
(x + 2) equal to 10.198039027 and -10.198039027.


Subproblem 1
x + 2 = 10.198039027

Simplifying
x + 2 = 10.198039027

Reorder the terms:
2 + x = 10.198039027

Solving
2 + x = 10.198039027

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 = 10.198039027 + -2

Combine like terms: 2 + -2 = 0
0 + x = 10.198039027 + -2
x = 10.198039027 + -2

Combine like terms: 10.198039027 + -2 = 8.198039027
x = 8.198039027

Simplifying
x = 8.198039027


Subproblem 2
x + 2 = -10.198039027

Simplifying
x + 2 = -10.198039027

Reorder the terms:
2 + x = -10.198039027

Solving
2 + x = -10.198039027

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 = -10.198039027 + -2

Combine like terms: 2 + -2 = 0
0 + x = -10.198039027 + -2
x = -10.198039027 + -2

Combine like terms: -10.198039027 + -2 = -12.198039027
x = -12.198039027

Simplifying
x = -12.198039027


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.198039027, -12.198039027}
Solution
x = {8.198039027, -12.198039027}

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