0.5x^2+5x-52=0

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Solution for 0.5x^2+5x-52=0 equation: 


Simplifying
0.5x2 + 5x + -52 = 0

Reorder the terms:
-52 + 5x + 0.5x2 = 0

Solving
-52 + 5x + 0.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.5 the coefficient of the squared term: 

Divide each side by '0.5'.
-104 + 10x + x2 = 0

Move the constant term to the right:

Add '104' to each side of the equation.
-104 + 10x + 104 + x2 = 0 + 104

Reorder the terms:
-104 + 104 + 10x + x2 = 0 + 104

Combine like terms: -104 + 104 = 0
0 + 10x + x2 = 0 + 104
10x + x2 = 0 + 104

Combine like terms: 0 + 104 = 104
10x + x2 = 104

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 = 104 + 25

Reorder the terms:
25 + 10x + x2 = 104 + 25

Combine like terms: 104 + 25 = 129
25 + 10x + x2 = 129

Factor a perfect square on the left side:
(x + 5)(x + 5) = 129

Calculate the square root of the right side: 11.357816692

Break this problem into two subproblems by setting 
(x + 5) equal to 11.357816692 and -11.357816692.


Subproblem 1
x + 5 = 11.357816692

Simplifying
x + 5 = 11.357816692

Reorder the terms:
5 + x = 11.357816692

Solving
5 + x = 11.357816692

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 = 11.357816692 + -5

Combine like terms: 5 + -5 = 0
0 + x = 11.357816692 + -5
x = 11.357816692 + -5

Combine like terms: 11.357816692 + -5 = 6.357816692
x = 6.357816692

Simplifying
x = 6.357816692


Subproblem 2
x + 5 = -11.357816692

Simplifying
x + 5 = -11.357816692

Reorder the terms:
5 + x = -11.357816692

Solving
5 + x = -11.357816692

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 = -11.357816692 + -5

Combine like terms: 5 + -5 = 0
0 + x = -11.357816692 + -5
x = -11.357816692 + -5

Combine like terms: -11.357816692 + -5 = -16.357816692
x = -16.357816692

Simplifying
x = -16.357816692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.357816692, -16.357816692}

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