-16x^2+64x-14=0

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Solution for -16x^2+64x-14=0 equation: 


Simplifying
-16x2 + 64x + -14 = 0

Reorder the terms:
-14 + 64x + -16x2 = 0

Solving
-14 + 64x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 32x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 32x + -8x2)' equal to zero and attempt to solve:

Simplifying
-7 + 32x + -8x2 = 0

Solving
-7 + 32x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.875 + -4x + x2 = 0

Move the constant term to the right:

Add '-0.875' to each side of the equation.
0.875 + -4x + -0.875 + x2 = 0 + -0.875

Reorder the terms:
0.875 + -0.875 + -4x + x2 = 0 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + -4x + x2 = 0 + -0.875
-4x + x2 = 0 + -0.875

Combine like terms: 0 + -0.875 = -0.875
-4x + x2 = -0.875

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -0.875 + 4

Reorder the terms:
4 + -4x + x2 = -0.875 + 4

Combine like terms: -0.875 + 4 = 3.125
4 + -4x + x2 = 3.125

Factor a perfect square on the left side:
(x + -2)(x + -2) = 3.125

Calculate the square root of the right side: 1.767766953

Break this problem into two subproblems by setting 
(x + -2) equal to 1.767766953 and -1.767766953.


Subproblem 1
x + -2 = 1.767766953

Simplifying
x + -2 = 1.767766953

Reorder the terms:
-2 + x = 1.767766953

Solving
-2 + x = 1.767766953

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 1.767766953 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.767766953 + 2
x = 1.767766953 + 2

Combine like terms: 1.767766953 + 2 = 3.767766953
x = 3.767766953

Simplifying
x = 3.767766953


Subproblem 2
x + -2 = -1.767766953

Simplifying
x + -2 = -1.767766953

Reorder the terms:
-2 + x = -1.767766953

Solving
-2 + x = -1.767766953

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -1.767766953 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.767766953 + 2
x = -1.767766953 + 2

Combine like terms: -1.767766953 + 2 = 0.232233047
x = 0.232233047

Simplifying
x = 0.232233047


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.767766953, 0.232233047}
Solution
x = {3.767766953, 0.232233047}

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