8x^2+134x-189=0

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Solution for 8x^2+134x-189=0 equation: 


Simplifying
8x2 + 134x + -189 = 0

Reorder the terms:
-189 + 134x + 8x2 = 0

Solving
-189 + 134x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-23.625 + 16.75x + x2 = 0

Move the constant term to the right:

Add '23.625' to each side of the equation.
-23.625 + 16.75x + 23.625 + x2 = 0 + 23.625

Reorder the terms:
-23.625 + 23.625 + 16.75x + x2 = 0 + 23.625

Combine like terms: -23.625 + 23.625 = 0.000
0.000 + 16.75x + x2 = 0 + 23.625
16.75x + x2 = 0 + 23.625

Combine like terms: 0 + 23.625 = 23.625
16.75x + x2 = 23.625

The x term is 16.75x.  Take half its coefficient (8.375).
Square it (70.140625) and add it to both sides.

Add '70.140625' to each side of the equation.
16.75x + 70.140625 + x2 = 23.625 + 70.140625

Reorder the terms:
70.140625 + 16.75x + x2 = 23.625 + 70.140625

Combine like terms: 23.625 + 70.140625 = 93.765625
70.140625 + 16.75x + x2 = 93.765625

Factor a perfect square on the left side:
(x + 8.375)(x + 8.375) = 93.765625

Calculate the square root of the right side: 9.683265203

Break this problem into two subproblems by setting 
(x + 8.375) equal to 9.683265203 and -9.683265203.


Subproblem 1
x + 8.375 = 9.683265203

Simplifying
x + 8.375 = 9.683265203

Reorder the terms:
8.375 + x = 9.683265203

Solving
8.375 + x = 9.683265203

Solving for variable 'x'.

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

Add '-8.375' to each side of the equation.
8.375 + -8.375 + x = 9.683265203 + -8.375

Combine like terms: 8.375 + -8.375 = 0.000
0.000 + x = 9.683265203 + -8.375
x = 9.683265203 + -8.375

Combine like terms: 9.683265203 + -8.375 = 1.308265203
x = 1.308265203

Simplifying
x = 1.308265203


Subproblem 2
x + 8.375 = -9.683265203

Simplifying
x + 8.375 = -9.683265203

Reorder the terms:
8.375 + x = -9.683265203

Solving
8.375 + x = -9.683265203

Solving for variable 'x'.

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

Add '-8.375' to each side of the equation.
8.375 + -8.375 + x = -9.683265203 + -8.375

Combine like terms: 8.375 + -8.375 = 0.000
0.000 + x = -9.683265203 + -8.375
x = -9.683265203 + -8.375

Combine like terms: -9.683265203 + -8.375 = -18.058265203
x = -18.058265203

Simplifying
x = -18.058265203


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.308265203, -18.058265203}

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