0.628x^2+6.28x-60.3=0

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Solution for 0.628x^2+6.28x-60.3=0 equation: 


Simplifying
0.628x2 + 6.28x + -60.3 = 0

Reorder the terms:
-60.3 + 6.28x + 0.628x2 = 0

Solving
-60.3 + 6.28x + 0.628x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.628'.
-96.01910828 + 10x + x2 = 0

Move the constant term to the right:

Add '96.01910828' to each side of the equation.
-96.01910828 + 10x + 96.01910828 + x2 = 0 + 96.01910828

Reorder the terms:
-96.01910828 + 96.01910828 + 10x + x2 = 0 + 96.01910828

Combine like terms: -96.01910828 + 96.01910828 = 0.00000000
0.00000000 + 10x + x2 = 0 + 96.01910828
10x + x2 = 0 + 96.01910828

Combine like terms: 0 + 96.01910828 = 96.01910828
10x + x2 = 96.01910828

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 = 96.01910828 + 25

Reorder the terms:
25 + 10x + x2 = 96.01910828 + 25

Combine like terms: 96.01910828 + 25 = 121.01910828
25 + 10x + x2 = 121.01910828

Factor a perfect square on the left side:
(x + 5)(x + 5) = 121.01910828

Calculate the square root of the right side: 11.000868524

Break this problem into two subproblems by setting 
(x + 5) equal to 11.000868524 and -11.000868524.


Subproblem 1
x + 5 = 11.000868524

Simplifying
x + 5 = 11.000868524

Reorder the terms:
5 + x = 11.000868524

Solving
5 + x = 11.000868524

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 = 11.000868524 + -5

Combine like terms: 5 + -5 = 0
0 + x = 11.000868524 + -5
x = 11.000868524 + -5

Combine like terms: 11.000868524 + -5 = 6.000868524
x = 6.000868524

Simplifying
x = 6.000868524


Subproblem 2
x + 5 = -11.000868524

Simplifying
x + 5 = -11.000868524

Reorder the terms:
5 + x = -11.000868524

Solving
5 + x = -11.000868524

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 = -11.000868524 + -5

Combine like terms: 5 + -5 = 0
0 + x = -11.000868524 + -5
x = -11.000868524 + -5

Combine like terms: -11.000868524 + -5 = -16.000868524
x = -16.000868524

Simplifying
x = -16.000868524


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.000868524, -16.000868524}

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