64x^2+14x-8=0

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Solution for 64x^2+14x-8=0 equation: 


Simplifying
64x2 + 14x + -8 = 0

Reorder the terms:
-8 + 14x + 64x2 = 0

Solving
-8 + 14x + 64x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 7x + 32x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + 7x + 32x2)' equal to zero and attempt to solve:

Simplifying
-4 + 7x + 32x2 = 0

Solving
-4 + 7x + 32x2 = 0

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

Divide each side by '32'.
-0.125 + 0.21875x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 0.21875x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 0.21875x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 0.21875x + x2 = 0 + 0.125
0.21875x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
0.21875x + x2 = 0.125

The x term is 0.21875x.  Take half its coefficient (0.109375).
Square it (0.01196289063) and add it to both sides.

Add '0.01196289063' to each side of the equation.
0.21875x + 0.01196289063 + x2 = 0.125 + 0.01196289063

Reorder the terms:
0.01196289063 + 0.21875x + x2 = 0.125 + 0.01196289063

Combine like terms: 0.125 + 0.01196289063 = 0.13696289063
0.01196289063 + 0.21875x + x2 = 0.13696289063

Factor a perfect square on the left side:
(x + 0.109375)(x + 0.109375) = 0.13696289063

Calculate the square root of the right side: 0.370084978

Break this problem into two subproblems by setting 
(x + 0.109375) equal to 0.370084978 and -0.370084978.


Subproblem 1
x + 0.109375 = 0.370084978

Simplifying
x + 0.109375 = 0.370084978

Reorder the terms:
0.109375 + x = 0.370084978

Solving
0.109375 + x = 0.370084978

Solving for variable 'x'.

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

Add '-0.109375' to each side of the equation.
0.109375 + -0.109375 + x = 0.370084978 + -0.109375

Combine like terms: 0.109375 + -0.109375 = 0.000000
0.000000 + x = 0.370084978 + -0.109375
x = 0.370084978 + -0.109375

Combine like terms: 0.370084978 + -0.109375 = 0.260709978
x = 0.260709978

Simplifying
x = 0.260709978


Subproblem 2
x + 0.109375 = -0.370084978

Simplifying
x + 0.109375 = -0.370084978

Reorder the terms:
0.109375 + x = -0.370084978

Solving
0.109375 + x = -0.370084978

Solving for variable 'x'.

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

Add '-0.109375' to each side of the equation.
0.109375 + -0.109375 + x = -0.370084978 + -0.109375

Combine like terms: 0.109375 + -0.109375 = 0.000000
0.000000 + x = -0.370084978 + -0.109375
x = -0.370084978 + -0.109375

Combine like terms: -0.370084978 + -0.109375 = -0.479459978
x = -0.479459978

Simplifying
x = -0.479459978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.260709978, -0.479459978}
Solution
x = {0.260709978, -0.479459978}

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