288x+-20x^2=168

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Solution for 288x+-20x^2=168 equation: 


Simplifying
288x + -20x2 = 168

Solving
288x + -20x2 = 168

Solving for variable 'x'.

Reorder the terms:
-168 + 288x + -20x2 = 168 + -168

Combine like terms: 168 + -168 = 0
-168 + 288x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-42 + 72x + -5x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-42 + 72x + -5x2)' equal to zero and attempt to solve:

Simplifying
-42 + 72x + -5x2 = 0

Solving
-42 + 72x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
8.4 + -14.4x + x2 = 0

Move the constant term to the right:

Add '-8.4' to each side of the equation.
8.4 + -14.4x + -8.4 + x2 = 0 + -8.4

Reorder the terms:
8.4 + -8.4 + -14.4x + x2 = 0 + -8.4

Combine like terms: 8.4 + -8.4 = 0.0
0.0 + -14.4x + x2 = 0 + -8.4
-14.4x + x2 = 0 + -8.4

Combine like terms: 0 + -8.4 = -8.4
-14.4x + x2 = -8.4

The x term is -14.4x.  Take half its coefficient (-7.2).
Square it (51.84) and add it to both sides.

Add '51.84' to each side of the equation.
-14.4x + 51.84 + x2 = -8.4 + 51.84

Reorder the terms:
51.84 + -14.4x + x2 = -8.4 + 51.84

Combine like terms: -8.4 + 51.84 = 43.44
51.84 + -14.4x + x2 = 43.44

Factor a perfect square on the left side:
(x + -7.2)(x + -7.2) = 43.44

Calculate the square root of the right side: 6.590902821

Break this problem into two subproblems by setting 
(x + -7.2) equal to 6.590902821 and -6.590902821.


Subproblem 1
x + -7.2 = 6.590902821

Simplifying
x + -7.2 = 6.590902821

Reorder the terms:
-7.2 + x = 6.590902821

Solving
-7.2 + x = 6.590902821

Solving for variable 'x'.

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

Add '7.2' to each side of the equation.
-7.2 + 7.2 + x = 6.590902821 + 7.2

Combine like terms: -7.2 + 7.2 = 0.0
0.0 + x = 6.590902821 + 7.2
x = 6.590902821 + 7.2

Combine like terms: 6.590902821 + 7.2 = 13.790902821
x = 13.790902821

Simplifying
x = 13.790902821


Subproblem 2
x + -7.2 = -6.590902821

Simplifying
x + -7.2 = -6.590902821

Reorder the terms:
-7.2 + x = -6.590902821

Solving
-7.2 + x = -6.590902821

Solving for variable 'x'.

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

Add '7.2' to each side of the equation.
-7.2 + 7.2 + x = -6.590902821 + 7.2

Combine like terms: -7.2 + 7.2 = 0.0
0.0 + x = -6.590902821 + 7.2
x = -6.590902821 + 7.2

Combine like terms: -6.590902821 + 7.2 = 0.609097179
x = 0.609097179

Simplifying
x = 0.609097179


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.790902821, 0.609097179}
Solution
x = {13.790902821, 0.609097179}

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