16x^2-90x-288=252

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Solution for 16x^2-90x-288=252 equation: 


Simplifying
16x2 + -90x + -288 = 252

Reorder the terms:
-288 + -90x + 16x2 = 252

Solving
-288 + -90x + 16x2 = 252

Solving for variable 'x'.

Reorder the terms:
-288 + -252 + -90x + 16x2 = 252 + -252

Combine like terms: -288 + -252 = -540
-540 + -90x + 16x2 = 252 + -252

Combine like terms: 252 + -252 = 0
-540 + -90x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-270 + -45x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-270 + -45x + 8x2)' equal to zero and attempt to solve:

Simplifying
-270 + -45x + 8x2 = 0

Solving
-270 + -45x + 8x2 = 0

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

Divide each side by '8'.
-33.75 + -5.625x + x2 = 0

Move the constant term to the right:

Add '33.75' to each side of the equation.
-33.75 + -5.625x + 33.75 + x2 = 0 + 33.75

Reorder the terms:
-33.75 + 33.75 + -5.625x + x2 = 0 + 33.75

Combine like terms: -33.75 + 33.75 = 0.00
0.00 + -5.625x + x2 = 0 + 33.75
-5.625x + x2 = 0 + 33.75

Combine like terms: 0 + 33.75 = 33.75
-5.625x + x2 = 33.75

The x term is -5.625x.  Take half its coefficient (-2.8125).
Square it (7.91015625) and add it to both sides.

Add '7.91015625' to each side of the equation.
-5.625x + 7.91015625 + x2 = 33.75 + 7.91015625

Reorder the terms:
7.91015625 + -5.625x + x2 = 33.75 + 7.91015625

Combine like terms: 33.75 + 7.91015625 = 41.66015625
7.91015625 + -5.625x + x2 = 41.66015625

Factor a perfect square on the left side:
(x + -2.8125)(x + -2.8125) = 41.66015625

Calculate the square root of the right side: 6.454467929

Break this problem into two subproblems by setting 
(x + -2.8125) equal to 6.454467929 and -6.454467929.


Subproblem 1
x + -2.8125 = 6.454467929

Simplifying
x + -2.8125 = 6.454467929

Reorder the terms:
-2.8125 + x = 6.454467929

Solving
-2.8125 + x = 6.454467929

Solving for variable 'x'.

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

Add '2.8125' to each side of the equation.
-2.8125 + 2.8125 + x = 6.454467929 + 2.8125

Combine like terms: -2.8125 + 2.8125 = 0.0000
0.0000 + x = 6.454467929 + 2.8125
x = 6.454467929 + 2.8125

Combine like terms: 6.454467929 + 2.8125 = 9.266967929
x = 9.266967929

Simplifying
x = 9.266967929


Subproblem 2
x + -2.8125 = -6.454467929

Simplifying
x + -2.8125 = -6.454467929

Reorder the terms:
-2.8125 + x = -6.454467929

Solving
-2.8125 + x = -6.454467929

Solving for variable 'x'.

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

Add '2.8125' to each side of the equation.
-2.8125 + 2.8125 + x = -6.454467929 + 2.8125

Combine like terms: -2.8125 + 2.8125 = 0.0000
0.0000 + x = -6.454467929 + 2.8125
x = -6.454467929 + 2.8125

Combine like terms: -6.454467929 + 2.8125 = -3.641967929
x = -3.641967929

Simplifying
x = -3.641967929


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.266967929, -3.641967929}
Solution
x = {9.266967929, -3.641967929}

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