x^2+10x-54=0

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Solution for x^2+10x-54=0 equation: 


Simplifying
x2 + 10x + -54 = 0

Reorder the terms:
-54 + 10x + x2 = 0

Solving
-54 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 10x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 10x + x2 = 0 + 54

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

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

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 = 54 + 25

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

Combine like terms: 54 + 25 = 79
25 + 10x + x2 = 79

Factor a perfect square on the left side:
(x + 5)(x + 5) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(x + 5) equal to 8.888194417 and -8.888194417.


Subproblem 1
x + 5 = 8.888194417

Simplifying
x + 5 = 8.888194417

Reorder the terms:
5 + x = 8.888194417

Solving
5 + x = 8.888194417

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 = 8.888194417 + -5

Combine like terms: 5 + -5 = 0
0 + x = 8.888194417 + -5
x = 8.888194417 + -5

Combine like terms: 8.888194417 + -5 = 3.888194417
x = 3.888194417

Simplifying
x = 3.888194417


Subproblem 2
x + 5 = -8.888194417

Simplifying
x + 5 = -8.888194417

Reorder the terms:
5 + x = -8.888194417

Solving
5 + x = -8.888194417

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 = -8.888194417 + -5

Combine like terms: 5 + -5 = 0
0 + x = -8.888194417 + -5
x = -8.888194417 + -5

Combine like terms: -8.888194417 + -5 = -13.888194417
x = -13.888194417

Simplifying
x = -13.888194417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.888194417, -13.888194417}

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