-16x^2+72x+15=0

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Solution for -16x^2+72x+15=0 equation: 


Simplifying
-16x2 + 72x + 15 = 0

Reorder the terms:
15 + 72x + -16x2 = 0

Solving
15 + 72x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.9375 + -4.5x + x2 = 0

Move the constant term to the right:

Add '0.9375' to each side of the equation.
-0.9375 + -4.5x + 0.9375 + x2 = 0 + 0.9375

Reorder the terms:
-0.9375 + 0.9375 + -4.5x + x2 = 0 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + -4.5x + x2 = 0 + 0.9375
-4.5x + x2 = 0 + 0.9375

Combine like terms: 0 + 0.9375 = 0.9375
-4.5x + x2 = 0.9375

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 0.9375 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 0.9375 + 5.0625

Combine like terms: 0.9375 + 5.0625 = 6
5.0625 + -4.5x + x2 = 6

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + -2.25 = 2.449489743

Simplifying
x + -2.25 = 2.449489743

Reorder the terms:
-2.25 + x = 2.449489743

Solving
-2.25 + x = 2.449489743

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.449489743 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.449489743 + 2.25
x = 2.449489743 + 2.25

Combine like terms: 2.449489743 + 2.25 = 4.699489743
x = 4.699489743

Simplifying
x = 4.699489743


Subproblem 2
x + -2.25 = -2.449489743

Simplifying
x + -2.25 = -2.449489743

Reorder the terms:
-2.25 + x = -2.449489743

Solving
-2.25 + x = -2.449489743

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.449489743 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.449489743 + 2.25
x = -2.449489743 + 2.25

Combine like terms: -2.449489743 + 2.25 = -0.199489743
x = -0.199489743

Simplifying
x = -0.199489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.699489743, -0.199489743}

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