2x^2-2+10x-2=180

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Solution for 2x^2-2+10x-2=180 equation: 


Simplifying
2x2 + -2 + 10x + -2 = 180

Reorder the terms:
-2 + -2 + 10x + 2x2 = 180

Combine like terms: -2 + -2 = -4
-4 + 10x + 2x2 = 180

Solving
-4 + 10x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-4 + -180 + 10x + 2x2 = 180 + -180

Combine like terms: -4 + -180 = -184
-184 + 10x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-184 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-92 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-92 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-92 + 5x + x2 = 0

Solving
-92 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '92' to each side of the equation.
-92 + 5x + 92 + x2 = 0 + 92

Reorder the terms:
-92 + 92 + 5x + x2 = 0 + 92

Combine like terms: -92 + 92 = 0
0 + 5x + x2 = 0 + 92
5x + x2 = 0 + 92

Combine like terms: 0 + 92 = 92
5x + x2 = 92

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 92 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 92 + 6.25

Combine like terms: 92 + 6.25 = 98.25
6.25 + 5x + x2 = 98.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 98.25

Calculate the square root of the right side: 9.912113801

Break this problem into two subproblems by setting 
(x + 2.5) equal to 9.912113801 and -9.912113801.


Subproblem 1
x + 2.5 = 9.912113801

Simplifying
x + 2.5 = 9.912113801

Reorder the terms:
2.5 + x = 9.912113801

Solving
2.5 + x = 9.912113801

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 9.912113801 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 9.912113801 + -2.5
x = 9.912113801 + -2.5

Combine like terms: 9.912113801 + -2.5 = 7.412113801
x = 7.412113801

Simplifying
x = 7.412113801


Subproblem 2
x + 2.5 = -9.912113801

Simplifying
x + 2.5 = -9.912113801

Reorder the terms:
2.5 + x = -9.912113801

Solving
2.5 + x = -9.912113801

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -9.912113801 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -9.912113801 + -2.5
x = -9.912113801 + -2.5

Combine like terms: -9.912113801 + -2.5 = -12.412113801
x = -12.412113801

Simplifying
x = -12.412113801


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.412113801, -12.412113801}
Solution
x = {7.412113801, -12.412113801}

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