x^2+10x+25=54

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Solution for x^2+10x+25=54 equation: 


Simplifying
x2 + 10x + 25 = 54

Reorder the terms:
25 + 10x + x2 = 54

Solving
25 + 10x + x2 = 54

Solving for variable 'x'.

Reorder the terms:
25 + -54 + 10x + x2 = 54 + -54

Combine like terms: 25 + -54 = -29
-29 + 10x + x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-29 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 10x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + 10x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 10x + x2 = 0 + 29
10x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
10x + x2 = 29

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 29 + 25

Reorder the terms:
25 + 10x + x2 = 29 + 25

Combine like terms: 29 + 25 = 54
25 + 10x + x2 = 54

Factor a perfect square on the left side:
(x + 5)(x + 5) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(x + 5) equal to 7.348469228 and -7.348469228.


Subproblem 1
x + 5 = 7.348469228

Simplifying
x + 5 = 7.348469228

Reorder the terms:
5 + x = 7.348469228

Solving
5 + x = 7.348469228

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 7.348469228 + -5

Combine like terms: 5 + -5 = 0
0 + x = 7.348469228 + -5
x = 7.348469228 + -5

Combine like terms: 7.348469228 + -5 = 2.348469228
x = 2.348469228

Simplifying
x = 2.348469228


Subproblem 2
x + 5 = -7.348469228

Simplifying
x + 5 = -7.348469228

Reorder the terms:
5 + x = -7.348469228

Solving
5 + x = -7.348469228

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -7.348469228 + -5

Combine like terms: 5 + -5 = 0
0 + x = -7.348469228 + -5
x = -7.348469228 + -5

Combine like terms: -7.348469228 + -5 = -12.348469228
x = -12.348469228

Simplifying
x = -12.348469228


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.348469228, -12.348469228}

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