8x^2-14x-18=0

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Solution for 8x^2-14x-18=0 equation: 


Simplifying
8x2 + -14x + -18 = 0

Reorder the terms:
-18 + -14x + 8x2 = 0

Solving
-18 + -14x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -7x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -7x + 4x2)' equal to zero and attempt to solve:

Simplifying
-9 + -7x + 4x2 = 0

Solving
-9 + -7x + 4x2 = 0

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

Divide each side by '4'.
-2.25 + -1.75x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -1.75x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -1.75x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -1.75x + x2 = 0 + 2.25
-1.75x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-1.75x + x2 = 2.25

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 2.25 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 2.25 + 0.765625

Combine like terms: 2.25 + 0.765625 = 3.015625
0.765625 + -1.75x + x2 = 3.015625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 3.015625

Calculate the square root of the right side: 1.736555499

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.736555499 and -1.736555499.


Subproblem 1
x + -0.875 = 1.736555499

Simplifying
x + -0.875 = 1.736555499

Reorder the terms:
-0.875 + x = 1.736555499

Solving
-0.875 + x = 1.736555499

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 1.736555499 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 1.736555499 + 0.875
x = 1.736555499 + 0.875

Combine like terms: 1.736555499 + 0.875 = 2.611555499
x = 2.611555499

Simplifying
x = 2.611555499


Subproblem 2
x + -0.875 = -1.736555499

Simplifying
x + -0.875 = -1.736555499

Reorder the terms:
-0.875 + x = -1.736555499

Solving
-0.875 + x = -1.736555499

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -1.736555499 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -1.736555499 + 0.875
x = -1.736555499 + 0.875

Combine like terms: -1.736555499 + 0.875 = -0.861555499
x = -0.861555499

Simplifying
x = -0.861555499


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.611555499, -0.861555499}
Solution
x = {2.611555499, -0.861555499}

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