2x^2+10x+25=81

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Solution for 2x^2+10x+25=81 equation: 


Simplifying
2x2 + 10x + 25 = 81

Reorder the terms:
25 + 10x + 2x2 = 81

Solving
25 + 10x + 2x2 = 81

Solving for variable 'x'.

Reorder the terms:
25 + -81 + 10x + 2x2 = 81 + -81

Combine like terms: 25 + -81 = -56
-56 + 10x + 2x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-56 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-28 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-28 + 5x + x2 = 0

Solving
-28 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 5x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 5x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 5x + x2 = 0 + 28
5x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
5x + x2 = 28

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 = 28 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 28 + 6.25

Combine like terms: 28 + 6.25 = 34.25
6.25 + 5x + x2 = 34.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.852349955 and -5.852349955.


Subproblem 1
x + 2.5 = 5.852349955

Simplifying
x + 2.5 = 5.852349955

Reorder the terms:
2.5 + x = 5.852349955

Solving
2.5 + x = 5.852349955

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 = 5.852349955 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.852349955 + -2.5
x = 5.852349955 + -2.5

Combine like terms: 5.852349955 + -2.5 = 3.352349955
x = 3.352349955

Simplifying
x = 3.352349955


Subproblem 2
x + 2.5 = -5.852349955

Simplifying
x + 2.5 = -5.852349955

Reorder the terms:
2.5 + x = -5.852349955

Solving
2.5 + x = -5.852349955

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 = -5.852349955 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.852349955 + -2.5
x = -5.852349955 + -2.5

Combine like terms: -5.852349955 + -2.5 = -8.352349955
x = -8.352349955

Simplifying
x = -8.352349955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.352349955, -8.352349955}
Solution
x = {3.352349955, -8.352349955}

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