-16x^2+24x+20=0

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Solution for -16x^2+24x+20=0 equation: 


Simplifying
-16x2 + 24x + 20 = 0

Reorder the terms:
20 + 24x + -16x2 = 0

Solving
20 + 24x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 6x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + 6x + -4x2)' equal to zero and attempt to solve:

Simplifying
5 + 6x + -4x2 = 0

Solving
5 + 6x + -4x2 = 0

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

Divide each side by '-4'.
-1.25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1.5x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1.5x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1.5x + x2 = 0 + 1.25
-1.5x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1.5x + x2 = 1.25

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 = 1.25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 1.25 + 0.5625

Combine like terms: 1.25 + 0.5625 = 1.8125
0.5625 + -1.5x + x2 = 1.8125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.346291202 and -1.346291202.


Subproblem 1
x + -0.75 = 1.346291202

Simplifying
x + -0.75 = 1.346291202

Reorder the terms:
-0.75 + x = 1.346291202

Solving
-0.75 + x = 1.346291202

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 = 1.346291202 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.346291202 + 0.75
x = 1.346291202 + 0.75

Combine like terms: 1.346291202 + 0.75 = 2.096291202
x = 2.096291202

Simplifying
x = 2.096291202


Subproblem 2
x + -0.75 = -1.346291202

Simplifying
x + -0.75 = -1.346291202

Reorder the terms:
-0.75 + x = -1.346291202

Solving
-0.75 + x = -1.346291202

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 = -1.346291202 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.346291202 + 0.75
x = -1.346291202 + 0.75

Combine like terms: -1.346291202 + 0.75 = -0.596291202
x = -0.596291202

Simplifying
x = -0.596291202


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.096291202, -0.596291202}
Solution
x = {2.096291202, -0.596291202}

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