5x^2+10x+25=110

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Solution for 5x^2+10x+25=110 equation: 


Simplifying
5x2 + 10x + 25 = 110

Reorder the terms:
25 + 10x + 5x2 = 110

Solving
25 + 10x + 5x2 = 110

Solving for variable 'x'.

Reorder the terms:
25 + -110 + 10x + 5x2 = 110 + -110

Combine like terms: 25 + -110 = -85
-85 + 10x + 5x2 = 110 + -110

Combine like terms: 110 + -110 = 0
-85 + 10x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-17 + 2x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-17 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-17 + 2x + x2 = 0

Solving
-17 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 2x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 2x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 2x + x2 = 0 + 17
2x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
2x + x2 = 17

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 17 + 1

Reorder the terms:
1 + 2x + x2 = 17 + 1

Combine like terms: 17 + 1 = 18
1 + 2x + x2 = 18

Factor a perfect square on the left side:
(x + 1)(x + 1) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 1) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + 1 = 4.242640687

Simplifying
x + 1 = 4.242640687

Reorder the terms:
1 + x = 4.242640687

Solving
1 + x = 4.242640687

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 4.242640687 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.242640687 + -1
x = 4.242640687 + -1

Combine like terms: 4.242640687 + -1 = 3.242640687
x = 3.242640687

Simplifying
x = 3.242640687


Subproblem 2
x + 1 = -4.242640687

Simplifying
x + 1 = -4.242640687

Reorder the terms:
1 + x = -4.242640687

Solving
1 + x = -4.242640687

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -4.242640687 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.242640687 + -1
x = -4.242640687 + -1

Combine like terms: -4.242640687 + -1 = -5.242640687
x = -5.242640687

Simplifying
x = -5.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.242640687, -5.242640687}
Solution
x = {3.242640687, -5.242640687}

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