-64x^2+120x-42=0

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Solution for -64x^2+120x-42=0 equation: 


Simplifying
-64x2 + 120x + -42 = 0

Reorder the terms:
-42 + 120x + -64x2 = 0

Solving
-42 + 120x + -64x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 60x + -32x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-21 + 60x + -32x2)' equal to zero and attempt to solve:

Simplifying
-21 + 60x + -32x2 = 0

Solving
-21 + 60x + -32x2 = 0

Begin completing the square.  Divide all terms by
-32 the coefficient of the squared term: 

Divide each side by '-32'.
0.65625 + -1.875x + x2 = 0

Move the constant term to the right:

Add '-0.65625' to each side of the equation.
0.65625 + -1.875x + -0.65625 + x2 = 0 + -0.65625

Reorder the terms:
0.65625 + -0.65625 + -1.875x + x2 = 0 + -0.65625

Combine like terms: 0.65625 + -0.65625 = 0.00000
0.00000 + -1.875x + x2 = 0 + -0.65625
-1.875x + x2 = 0 + -0.65625

Combine like terms: 0 + -0.65625 = -0.65625
-1.875x + x2 = -0.65625

The x term is -1.875x.  Take half its coefficient (-0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
-1.875x + 0.87890625 + x2 = -0.65625 + 0.87890625

Reorder the terms:
0.87890625 + -1.875x + x2 = -0.65625 + 0.87890625

Combine like terms: -0.65625 + 0.87890625 = 0.22265625
0.87890625 + -1.875x + x2 = 0.22265625

Factor a perfect square on the left side:
(x + -0.9375)(x + -0.9375) = 0.22265625

Calculate the square root of the right side: 0.471864652

Break this problem into two subproblems by setting 
(x + -0.9375) equal to 0.471864652 and -0.471864652.


Subproblem 1
x + -0.9375 = 0.471864652

Simplifying
x + -0.9375 = 0.471864652

Reorder the terms:
-0.9375 + x = 0.471864652

Solving
-0.9375 + x = 0.471864652

Solving for variable 'x'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + x = 0.471864652 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + x = 0.471864652 + 0.9375
x = 0.471864652 + 0.9375

Combine like terms: 0.471864652 + 0.9375 = 1.409364652
x = 1.409364652

Simplifying
x = 1.409364652


Subproblem 2
x + -0.9375 = -0.471864652

Simplifying
x + -0.9375 = -0.471864652

Reorder the terms:
-0.9375 + x = -0.471864652

Solving
-0.9375 + x = -0.471864652

Solving for variable 'x'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + x = -0.471864652 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + x = -0.471864652 + 0.9375
x = -0.471864652 + 0.9375

Combine like terms: -0.471864652 + 0.9375 = 0.465635348
x = 0.465635348

Simplifying
x = 0.465635348


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.409364652, 0.465635348}
Solution
x = {1.409364652, 0.465635348}

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