16x^2-60x-288=0

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Solution for 16x^2-60x-288=0 equation: 


Simplifying
16x2 + -60x + -288 = 0

Reorder the terms:
-288 + -60x + 16x2 = 0

Solving
-288 + -60x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-72 + -15x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-72 + -15x + 4x2)' equal to zero and attempt to solve:

Simplifying
-72 + -15x + 4x2 = 0

Solving
-72 + -15x + 4x2 = 0

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

Divide each side by '4'.
-18 + -3.75x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -3.75x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -3.75x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -3.75x + x2 = 0 + 18
-3.75x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-3.75x + x2 = 18

The x term is -3.75x.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75x + 3.515625 + x2 = 18 + 3.515625

Reorder the terms:
3.515625 + -3.75x + x2 = 18 + 3.515625

Combine like terms: 18 + 3.515625 = 21.515625
3.515625 + -3.75x + x2 = 21.515625

Factor a perfect square on the left side:
(x + -1.875)(x + -1.875) = 21.515625

Calculate the square root of the right side: 4.638493829

Break this problem into two subproblems by setting 
(x + -1.875) equal to 4.638493829 and -4.638493829.


Subproblem 1
x + -1.875 = 4.638493829

Simplifying
x + -1.875 = 4.638493829

Reorder the terms:
-1.875 + x = 4.638493829

Solving
-1.875 + x = 4.638493829

Solving for variable 'x'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x = 4.638493829 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x = 4.638493829 + 1.875
x = 4.638493829 + 1.875

Combine like terms: 4.638493829 + 1.875 = 6.513493829
x = 6.513493829

Simplifying
x = 6.513493829


Subproblem 2
x + -1.875 = -4.638493829

Simplifying
x + -1.875 = -4.638493829

Reorder the terms:
-1.875 + x = -4.638493829

Solving
-1.875 + x = -4.638493829

Solving for variable 'x'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x = -4.638493829 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x = -4.638493829 + 1.875
x = -4.638493829 + 1.875

Combine like terms: -4.638493829 + 1.875 = -2.763493829
x = -2.763493829

Simplifying
x = -2.763493829


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.513493829, -2.763493829}
Solution
x = {6.513493829, -2.763493829}

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