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

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


Simplifying
-16x2 + 64x + 2 = 0

Reorder the terms:
2 + 64x + -16x2 = 0

Solving
2 + 64x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 32x + -8x2) = 0

Ignore the factor 2.

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

Simplifying
1 + 32x + -8x2 = 0

Solving
1 + 32x + -8x2 = 0

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

Divide each side by '-8'.
-0.125 + -4x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -4x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -4x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -4x + x2 = 0 + 0.125
-4x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-4x + x2 = 0.125

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 = 0.125 + 4

Reorder the terms:
4 + -4x + x2 = 0.125 + 4

Combine like terms: 0.125 + 4 = 4.125
4 + -4x + x2 = 4.125

Factor a perfect square on the left side:
(x + -2)(x + -2) = 4.125

Calculate the square root of the right side: 2.031009601

Break this problem into two subproblems by setting 
(x + -2) equal to 2.031009601 and -2.031009601.


Subproblem 1
x + -2 = 2.031009601

Simplifying
x + -2 = 2.031009601

Reorder the terms:
-2 + x = 2.031009601

Solving
-2 + x = 2.031009601

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 = 2.031009601 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.031009601 + 2
x = 2.031009601 + 2

Combine like terms: 2.031009601 + 2 = 4.031009601
x = 4.031009601

Simplifying
x = 4.031009601


Subproblem 2
x + -2 = -2.031009601

Simplifying
x + -2 = -2.031009601

Reorder the terms:
-2 + x = -2.031009601

Solving
-2 + x = -2.031009601

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 = -2.031009601 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.031009601 + 2
x = -2.031009601 + 2

Combine like terms: -2.031009601 + 2 = -0.031009601
x = -0.031009601

Simplifying
x = -0.031009601


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.031009601, -0.031009601}
Solution
x = {4.031009601, -0.031009601}

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