8x^2-16x-62=0

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Solution for 8x^2-16x-62=0 equation: 


Simplifying
8x2 + -16x + -62 = 0

Reorder the terms:
-62 + -16x + 8x2 = 0

Solving
-62 + -16x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-31 + -8x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-31 + -8x + 4x2)' equal to zero and attempt to solve:

Simplifying
-31 + -8x + 4x2 = 0

Solving
-31 + -8x + 4x2 = 0

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

Divide each side by '4'.
-7.75 + -2x + x2 = 0

Move the constant term to the right:

Add '7.75' to each side of the equation.
-7.75 + -2x + 7.75 + x2 = 0 + 7.75

Reorder the terms:
-7.75 + 7.75 + -2x + x2 = 0 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + -2x + x2 = 0 + 7.75
-2x + x2 = 0 + 7.75

Combine like terms: 0 + 7.75 = 7.75
-2x + x2 = 7.75

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 7.75 + 1

Reorder the terms:
1 + -2x + x2 = 7.75 + 1

Combine like terms: 7.75 + 1 = 8.75
1 + -2x + x2 = 8.75

Factor a perfect square on the left side:
(x + -1)(x + -1) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(x + -1) equal to 2.958039892 and -2.958039892.


Subproblem 1
x + -1 = 2.958039892

Simplifying
x + -1 = 2.958039892

Reorder the terms:
-1 + x = 2.958039892

Solving
-1 + x = 2.958039892

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 2.958039892 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.958039892 + 1
x = 2.958039892 + 1

Combine like terms: 2.958039892 + 1 = 3.958039892
x = 3.958039892

Simplifying
x = 3.958039892


Subproblem 2
x + -1 = -2.958039892

Simplifying
x + -1 = -2.958039892

Reorder the terms:
-1 + x = -2.958039892

Solving
-1 + x = -2.958039892

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -2.958039892 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.958039892 + 1
x = -2.958039892 + 1

Combine like terms: -2.958039892 + 1 = -1.958039892
x = -1.958039892

Simplifying
x = -1.958039892


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.958039892, -1.958039892}
Solution
x = {3.958039892, -1.958039892}

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