-6x^2+53.4x+1048.8=0

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Solution for -6x^2+53.4x+1048.8=0 equation: 


Simplifying
-6x2 + 53.4x + 1048.8 = 0

Reorder the terms:
1048.8 + 53.4x + -6x2 = 0

Solving
1048.8 + 53.4x + -6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-174.8 + -8.9x + x2 = 0

Move the constant term to the right:

Add '174.8' to each side of the equation.
-174.8 + -8.9x + 174.8 + x2 = 0 + 174.8

Reorder the terms:
-174.8 + 174.8 + -8.9x + x2 = 0 + 174.8

Combine like terms: -174.8 + 174.8 = 0.0
0.0 + -8.9x + x2 = 0 + 174.8
-8.9x + x2 = 0 + 174.8

Combine like terms: 0 + 174.8 = 174.8
-8.9x + x2 = 174.8

The x term is -8.9x.  Take half its coefficient (-4.45).
Square it (19.8025) and add it to both sides.

Add '19.8025' to each side of the equation.
-8.9x + 19.8025 + x2 = 174.8 + 19.8025

Reorder the terms:
19.8025 + -8.9x + x2 = 174.8 + 19.8025

Combine like terms: 174.8 + 19.8025 = 194.6025
19.8025 + -8.9x + x2 = 194.6025

Factor a perfect square on the left side:
(x + -4.45)(x + -4.45) = 194.6025

Calculate the square root of the right side: 13.95

Break this problem into two subproblems by setting 
(x + -4.45) equal to 13.95 and -13.95.


Subproblem 1
x + -4.45 = 13.95

Simplifying
x + -4.45 = 13.95

Reorder the terms:
-4.45 + x = 13.95

Solving
-4.45 + x = 13.95

Solving for variable 'x'.

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

Add '4.45' to each side of the equation.
-4.45 + 4.45 + x = 13.95 + 4.45

Combine like terms: -4.45 + 4.45 = 0.00
0.00 + x = 13.95 + 4.45
x = 13.95 + 4.45

Combine like terms: 13.95 + 4.45 = 18.4
x = 18.4

Simplifying
x = 18.4


Subproblem 2
x + -4.45 = -13.95

Simplifying
x + -4.45 = -13.95

Reorder the terms:
-4.45 + x = -13.95

Solving
-4.45 + x = -13.95

Solving for variable 'x'.

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

Add '4.45' to each side of the equation.
-4.45 + 4.45 + x = -13.95 + 4.45

Combine like terms: -4.45 + 4.45 = 0.00
0.00 + x = -13.95 + 4.45
x = -13.95 + 4.45

Combine like terms: -13.95 + 4.45 = -9.5
x = -9.5

Simplifying
x = -9.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.4, -9.5}

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