x^2+20x+25=7

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Solution for x^2+20x+25=7 equation: 


Simplifying
x2 + 20x + 25 = 7

Reorder the terms:
25 + 20x + x2 = 7

Solving
25 + 20x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
25 + -7 + 20x + x2 = 7 + -7

Combine like terms: 25 + -7 = 18
18 + 20x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
18 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 20x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + 20x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 20x + x2 = 0 + -18
20x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
20x + x2 = -18

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -18 + 100

Reorder the terms:
100 + 20x + x2 = -18 + 100

Combine like terms: -18 + 100 = 82
100 + 20x + x2 = 82

Factor a perfect square on the left side:
(x + 10)(x + 10) = 82

Calculate the square root of the right side: 9.055385138

Break this problem into two subproblems by setting 
(x + 10) equal to 9.055385138 and -9.055385138.


Subproblem 1
x + 10 = 9.055385138

Simplifying
x + 10 = 9.055385138

Reorder the terms:
10 + x = 9.055385138

Solving
10 + x = 9.055385138

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 9.055385138 + -10

Combine like terms: 10 + -10 = 0
0 + x = 9.055385138 + -10
x = 9.055385138 + -10

Combine like terms: 9.055385138 + -10 = -0.944614862
x = -0.944614862

Simplifying
x = -0.944614862


Subproblem 2
x + 10 = -9.055385138

Simplifying
x + 10 = -9.055385138

Reorder the terms:
10 + x = -9.055385138

Solving
10 + x = -9.055385138

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -9.055385138 + -10

Combine like terms: 10 + -10 = 0
0 + x = -9.055385138 + -10
x = -9.055385138 + -10

Combine like terms: -9.055385138 + -10 = -19.055385138
x = -19.055385138

Simplifying
x = -19.055385138


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.944614862, -19.055385138}

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