16x^2+324x-356=0

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Solution for 16x^2+324x-356=0 equation: 


Simplifying
16x2 + 324x + -356 = 0

Reorder the terms:
-356 + 324x + 16x2 = 0

Solving
-356 + 324x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-89 + 81x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-89 + 81x + 4x2)' equal to zero and attempt to solve:

Simplifying
-89 + 81x + 4x2 = 0

Solving
-89 + 81x + 4x2 = 0

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

Divide each side by '4'.
-22.25 + 20.25x + x2 = 0

Move the constant term to the right:

Add '22.25' to each side of the equation.
-22.25 + 20.25x + 22.25 + x2 = 0 + 22.25

Reorder the terms:
-22.25 + 22.25 + 20.25x + x2 = 0 + 22.25

Combine like terms: -22.25 + 22.25 = 0.00
0.00 + 20.25x + x2 = 0 + 22.25
20.25x + x2 = 0 + 22.25

Combine like terms: 0 + 22.25 = 22.25
20.25x + x2 = 22.25

The x term is 20.25x.  Take half its coefficient (10.125).
Square it (102.515625) and add it to both sides.

Add '102.515625' to each side of the equation.
20.25x + 102.515625 + x2 = 22.25 + 102.515625

Reorder the terms:
102.515625 + 20.25x + x2 = 22.25 + 102.515625

Combine like terms: 22.25 + 102.515625 = 124.765625
102.515625 + 20.25x + x2 = 124.765625

Factor a perfect square on the left side:
(x + 10.125)(x + 10.125) = 124.765625

Calculate the square root of the right side: 11.169853401

Break this problem into two subproblems by setting 
(x + 10.125) equal to 11.169853401 and -11.169853401.


Subproblem 1
x + 10.125 = 11.169853401

Simplifying
x + 10.125 = 11.169853401

Reorder the terms:
10.125 + x = 11.169853401

Solving
10.125 + x = 11.169853401

Solving for variable 'x'.

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

Add '-10.125' to each side of the equation.
10.125 + -10.125 + x = 11.169853401 + -10.125

Combine like terms: 10.125 + -10.125 = 0.000
0.000 + x = 11.169853401 + -10.125
x = 11.169853401 + -10.125

Combine like terms: 11.169853401 + -10.125 = 1.044853401
x = 1.044853401

Simplifying
x = 1.044853401


Subproblem 2
x + 10.125 = -11.169853401

Simplifying
x + 10.125 = -11.169853401

Reorder the terms:
10.125 + x = -11.169853401

Solving
10.125 + x = -11.169853401

Solving for variable 'x'.

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

Add '-10.125' to each side of the equation.
10.125 + -10.125 + x = -11.169853401 + -10.125

Combine like terms: 10.125 + -10.125 = 0.000
0.000 + x = -11.169853401 + -10.125
x = -11.169853401 + -10.125

Combine like terms: -11.169853401 + -10.125 = -21.294853401
x = -21.294853401

Simplifying
x = -21.294853401


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.044853401, -21.294853401}
Solution
x = {1.044853401, -21.294853401}

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