-16x^2+20x+60=0

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Solution for -16x^2+20x+60=0 equation: 


Simplifying
-16x2 + 20x + 60 = 0

Reorder the terms:
60 + 20x + -16x2 = 0

Solving
60 + 20x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + 5x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(15 + 5x + -4x2)' equal to zero and attempt to solve:

Simplifying
15 + 5x + -4x2 = 0

Solving
15 + 5x + -4x2 = 0

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

Divide each side by '-4'.
-3.75 + -1.25x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -1.25x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -1.25x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -1.25x + x2 = 0 + 3.75
-1.25x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-1.25x + x2 = 3.75

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 3.75 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 3.75 + 0.390625

Combine like terms: 3.75 + 0.390625 = 4.140625
0.390625 + -1.25x + x2 = 4.140625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(x + -0.625) equal to 2.034852575 and -2.034852575.


Subproblem 1
x + -0.625 = 2.034852575

Simplifying
x + -0.625 = 2.034852575

Reorder the terms:
-0.625 + x = 2.034852575

Solving
-0.625 + x = 2.034852575

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 2.034852575 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 2.034852575 + 0.625
x = 2.034852575 + 0.625

Combine like terms: 2.034852575 + 0.625 = 2.659852575
x = 2.659852575

Simplifying
x = 2.659852575


Subproblem 2
x + -0.625 = -2.034852575

Simplifying
x + -0.625 = -2.034852575

Reorder the terms:
-0.625 + x = -2.034852575

Solving
-0.625 + x = -2.034852575

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -2.034852575 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -2.034852575 + 0.625
x = -2.034852575 + 0.625

Combine like terms: -2.034852575 + 0.625 = -1.409852575
x = -1.409852575

Simplifying
x = -1.409852575


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.659852575, -1.409852575}
Solution
x = {2.659852575, -1.409852575}

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