x^2+10.2x-54.99=0

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Solution for x^2+10.2x-54.99=0 equation: 


Simplifying
x2 + 10.2x + -54.99 = 0

Reorder the terms:
-54.99 + 10.2x + x2 = 0

Solving
-54.99 + 10.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '54.99' to each side of the equation.
-54.99 + 10.2x + 54.99 + x2 = 0 + 54.99

Reorder the terms:
-54.99 + 54.99 + 10.2x + x2 = 0 + 54.99

Combine like terms: -54.99 + 54.99 = 0.00
0.00 + 10.2x + x2 = 0 + 54.99
10.2x + x2 = 0 + 54.99

Combine like terms: 0 + 54.99 = 54.99
10.2x + x2 = 54.99

The x term is 10.2x.  Take half its coefficient (5.1).
Square it (26.01) and add it to both sides.

Add '26.01' to each side of the equation.
10.2x + 26.01 + x2 = 54.99 + 26.01

Reorder the terms:
26.01 + 10.2x + x2 = 54.99 + 26.01

Combine like terms: 54.99 + 26.01 = 81
26.01 + 10.2x + x2 = 81

Factor a perfect square on the left side:
(x + 5.1)(x + 5.1) = 81

Calculate the square root of the right side: 9

Break this problem into two subproblems by setting 
(x + 5.1) equal to 9 and -9.


Subproblem 1
x + 5.1 = 9

Simplifying
x + 5.1 = 9

Reorder the terms:
5.1 + x = 9

Solving
5.1 + x = 9

Solving for variable 'x'.

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

Add '-5.1' to each side of the equation.
5.1 + -5.1 + x = 9 + -5.1

Combine like terms: 5.1 + -5.1 = 0.0
0.0 + x = 9 + -5.1
x = 9 + -5.1

Combine like terms: 9 + -5.1 = 3.9
x = 3.9

Simplifying
x = 3.9


Subproblem 2
x + 5.1 = -9

Simplifying
x + 5.1 = -9

Reorder the terms:
5.1 + x = -9

Solving
5.1 + x = -9

Solving for variable 'x'.

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

Add '-5.1' to each side of the equation.
5.1 + -5.1 + x = -9 + -5.1

Combine like terms: 5.1 + -5.1 = 0.0
0.0 + x = -9 + -5.1
x = -9 + -5.1

Combine like terms: -9 + -5.1 = -14.1
x = -14.1

Simplifying
x = -14.1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.9, -14.1}

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