2(x*x)+10x=110

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Solution for 2(x*x)+10x=110 equation: 


Simplifying
2(x * x) + 10x = 110

Multiply x * x
2(x2) + 10x = 110

Reorder the terms:
10x + 2x2 = 110

Solving
10x + 2x2 = 110

Solving for variable 'x'.

Reorder the terms:
-110 + 10x + 2x2 = 110 + -110

Combine like terms: 110 + -110 = 0
-110 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-55 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-55 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-55 + 5x + x2 = 0

Solving
-55 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '55' to each side of the equation.
-55 + 5x + 55 + x2 = 0 + 55

Reorder the terms:
-55 + 55 + 5x + x2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 5x + x2 = 0 + 55
5x + x2 = 0 + 55

Combine like terms: 0 + 55 = 55
5x + x2 = 55

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 = 55 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 55 + 6.25

Combine like terms: 55 + 6.25 = 61.25
6.25 + 5x + x2 = 61.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 61.25

Calculate the square root of the right side: 7.826237921

Break this problem into two subproblems by setting 
(x + 2.5) equal to 7.826237921 and -7.826237921.


Subproblem 1
x + 2.5 = 7.826237921

Simplifying
x + 2.5 = 7.826237921

Reorder the terms:
2.5 + x = 7.826237921

Solving
2.5 + x = 7.826237921

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 = 7.826237921 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 7.826237921 + -2.5
x = 7.826237921 + -2.5

Combine like terms: 7.826237921 + -2.5 = 5.326237921
x = 5.326237921

Simplifying
x = 5.326237921


Subproblem 2
x + 2.5 = -7.826237921

Simplifying
x + 2.5 = -7.826237921

Reorder the terms:
2.5 + x = -7.826237921

Solving
2.5 + x = -7.826237921

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 = -7.826237921 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -7.826237921 + -2.5
x = -7.826237921 + -2.5

Combine like terms: -7.826237921 + -2.5 = -10.326237921
x = -10.326237921

Simplifying
x = -10.326237921


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.326237921, -10.326237921}
Solution
x = {5.326237921, -10.326237921}

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