x^2+10x+10=24

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Solution for x^2+10x+10=24 equation: 


Simplifying
x2 + 10x + 10 = 24

Reorder the terms:
10 + 10x + x2 = 24

Solving
10 + 10x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
10 + -24 + 10x + x2 = 24 + -24

Combine like terms: 10 + -24 = -14
-14 + 10x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-14 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 10x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 10x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 10x + x2 = 0 + 14
10x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
10x + x2 = 14

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 = 14 + 25

Reorder the terms:
25 + 10x + x2 = 14 + 25

Combine like terms: 14 + 25 = 39
25 + 10x + x2 = 39

Factor a perfect square on the left side:
(x + 5)(x + 5) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + 5) equal to 6.244997998 and -6.244997998.


Subproblem 1
x + 5 = 6.244997998

Simplifying
x + 5 = 6.244997998

Reorder the terms:
5 + x = 6.244997998

Solving
5 + x = 6.244997998

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 = 6.244997998 + -5

Combine like terms: 5 + -5 = 0
0 + x = 6.244997998 + -5
x = 6.244997998 + -5

Combine like terms: 6.244997998 + -5 = 1.244997998
x = 1.244997998

Simplifying
x = 1.244997998


Subproblem 2
x + 5 = -6.244997998

Simplifying
x + 5 = -6.244997998

Reorder the terms:
5 + x = -6.244997998

Solving
5 + x = -6.244997998

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 = -6.244997998 + -5

Combine like terms: 5 + -5 = 0
0 + x = -6.244997998 + -5
x = -6.244997998 + -5

Combine like terms: -6.244997998 + -5 = -11.244997998
x = -11.244997998

Simplifying
x = -11.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.244997998, -11.244997998}

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