-16x^2+12x+9=0

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Solution for -16x^2+12x+9=0 equation: 


Simplifying
-16x2 + 12x + 9 = 0

Reorder the terms:
9 + 12x + -16x2 = 0

Solving
9 + 12x + -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'.
-0.5625 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.5625' to each side of the equation.
-0.5625 + -0.75x + 0.5625 + x2 = 0 + 0.5625

Reorder the terms:
-0.5625 + 0.5625 + -0.75x + x2 = 0 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + -0.75x + x2 = 0 + 0.5625
-0.75x + x2 = 0 + 0.5625

Combine like terms: 0 + 0.5625 = 0.5625
-0.75x + x2 = 0.5625

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 0.5625 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 0.5625 + 0.140625

Combine like terms: 0.5625 + 0.140625 = 0.703125
0.140625 + -0.75x + x2 = 0.703125

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.703125

Calculate the square root of the right side: 0.838525492

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.838525492 and -0.838525492.


Subproblem 1
x + -0.375 = 0.838525492

Simplifying
x + -0.375 = 0.838525492

Reorder the terms:
-0.375 + x = 0.838525492

Solving
-0.375 + x = 0.838525492

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 0.838525492 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 0.838525492 + 0.375
x = 0.838525492 + 0.375

Combine like terms: 0.838525492 + 0.375 = 1.213525492
x = 1.213525492

Simplifying
x = 1.213525492


Subproblem 2
x + -0.375 = -0.838525492

Simplifying
x + -0.375 = -0.838525492

Reorder the terms:
-0.375 + x = -0.838525492

Solving
-0.375 + x = -0.838525492

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -0.838525492 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -0.838525492 + 0.375
x = -0.838525492 + 0.375

Combine like terms: -0.838525492 + 0.375 = -0.463525492
x = -0.463525492

Simplifying
x = -0.463525492


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.213525492, -0.463525492}

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