x^2+10.8x-153.5=0

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Solution for x^2+10.8x-153.5=0 equation: 


Simplifying
x2 + 10.8x + -153.5 = 0

Reorder the terms:
-153.5 + 10.8x + x2 = 0

Solving
-153.5 + 10.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '153.5' to each side of the equation.
-153.5 + 10.8x + 153.5 + x2 = 0 + 153.5

Reorder the terms:
-153.5 + 153.5 + 10.8x + x2 = 0 + 153.5

Combine like terms: -153.5 + 153.5 = 0.0
0.0 + 10.8x + x2 = 0 + 153.5
10.8x + x2 = 0 + 153.5

Combine like terms: 0 + 153.5 = 153.5
10.8x + x2 = 153.5

The x term is 10.8x.  Take half its coefficient (5.4).
Square it (29.16) and add it to both sides.

Add '29.16' to each side of the equation.
10.8x + 29.16 + x2 = 153.5 + 29.16

Reorder the terms:
29.16 + 10.8x + x2 = 153.5 + 29.16

Combine like terms: 153.5 + 29.16 = 182.66
29.16 + 10.8x + x2 = 182.66

Factor a perfect square on the left side:
(x + 5.4)(x + 5.4) = 182.66

Calculate the square root of the right side: 13.515176654

Break this problem into two subproblems by setting 
(x + 5.4) equal to 13.515176654 and -13.515176654.


Subproblem 1
x + 5.4 = 13.515176654

Simplifying
x + 5.4 = 13.515176654

Reorder the terms:
5.4 + x = 13.515176654

Solving
5.4 + x = 13.515176654

Solving for variable 'x'.

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

Add '-5.4' to each side of the equation.
5.4 + -5.4 + x = 13.515176654 + -5.4

Combine like terms: 5.4 + -5.4 = 0.0
0.0 + x = 13.515176654 + -5.4
x = 13.515176654 + -5.4

Combine like terms: 13.515176654 + -5.4 = 8.115176654
x = 8.115176654

Simplifying
x = 8.115176654


Subproblem 2
x + 5.4 = -13.515176654

Simplifying
x + 5.4 = -13.515176654

Reorder the terms:
5.4 + x = -13.515176654

Solving
5.4 + x = -13.515176654

Solving for variable 'x'.

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

Add '-5.4' to each side of the equation.
5.4 + -5.4 + x = -13.515176654 + -5.4

Combine like terms: 5.4 + -5.4 = 0.0
0.0 + x = -13.515176654 + -5.4
x = -13.515176654 + -5.4

Combine like terms: -13.515176654 + -5.4 = -18.915176654
x = -18.915176654

Simplifying
x = -18.915176654


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.115176654, -18.915176654}

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