8x^2+6x-16=0

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Solution for 8x^2+6x-16=0 equation: 


Simplifying
8x2 + 6x + -16 = 0

Reorder the terms:
-16 + 6x + 8x2 = 0

Solving
-16 + 6x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 3x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + 3x + 4x2)' equal to zero and attempt to solve:

Simplifying
-8 + 3x + 4x2 = 0

Solving
-8 + 3x + 4x2 = 0

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

Divide each side by '4'.
-2 + 0.75x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.75x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.75x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.75x + x2 = 0 + 2
0.75x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.75x + x2 = 2

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 2 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 2 + 0.140625

Combine like terms: 2 + 0.140625 = 2.140625
0.140625 + 0.75x + x2 = 2.140625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 2.140625

Calculate the square root of the right side: 1.463087489

Break this problem into two subproblems by setting 
(x + 0.375) equal to 1.463087489 and -1.463087489.


Subproblem 1
x + 0.375 = 1.463087489

Simplifying
x + 0.375 = 1.463087489

Reorder the terms:
0.375 + x = 1.463087489

Solving
0.375 + x = 1.463087489

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 1.463087489 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 1.463087489 + -0.375
x = 1.463087489 + -0.375

Combine like terms: 1.463087489 + -0.375 = 1.088087489
x = 1.088087489

Simplifying
x = 1.088087489


Subproblem 2
x + 0.375 = -1.463087489

Simplifying
x + 0.375 = -1.463087489

Reorder the terms:
0.375 + x = -1.463087489

Solving
0.375 + x = -1.463087489

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -1.463087489 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -1.463087489 + -0.375
x = -1.463087489 + -0.375

Combine like terms: -1.463087489 + -0.375 = -1.838087489
x = -1.838087489

Simplifying
x = -1.838087489


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.088087489, -1.838087489}
Solution
x = {1.088087489, -1.838087489}

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