-16x^2+24x+13.2=0

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Solution for -16x^2+24x+13.2=0 equation: 


Simplifying
-16x2 + 24x + 13.2 = 0

Reorder the terms:
13.2 + 24x + -16x2 = 0

Solving
13.2 + 24x + -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'.
-0.825 + -1.5x + x2 = 0

Move the constant term to the right:

Add '0.825' to each side of the equation.
-0.825 + -1.5x + 0.825 + x2 = 0 + 0.825

Reorder the terms:
-0.825 + 0.825 + -1.5x + x2 = 0 + 0.825

Combine like terms: -0.825 + 0.825 = 0.000
0.000 + -1.5x + x2 = 0 + 0.825
-1.5x + x2 = 0 + 0.825

Combine like terms: 0 + 0.825 = 0.825
-1.5x + x2 = 0.825

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 0.825 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 0.825 + 0.5625

Combine like terms: 0.825 + 0.5625 = 1.3875
0.5625 + -1.5x + x2 = 1.3875

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 1.3875

Calculate the square root of the right side: 1.177921899

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.177921899 and -1.177921899.


Subproblem 1
x + -0.75 = 1.177921899

Simplifying
x + -0.75 = 1.177921899

Reorder the terms:
-0.75 + x = 1.177921899

Solving
-0.75 + x = 1.177921899

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 1.177921899 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.177921899 + 0.75
x = 1.177921899 + 0.75

Combine like terms: 1.177921899 + 0.75 = 1.927921899
x = 1.927921899

Simplifying
x = 1.927921899


Subproblem 2
x + -0.75 = -1.177921899

Simplifying
x + -0.75 = -1.177921899

Reorder the terms:
-0.75 + x = -1.177921899

Solving
-0.75 + x = -1.177921899

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -1.177921899 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.177921899 + 0.75
x = -1.177921899 + 0.75

Combine like terms: -1.177921899 + 0.75 = -0.427921899
x = -0.427921899

Simplifying
x = -0.427921899


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.927921899, -0.427921899}

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