8x^2+86x+150=0

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Solution for 8x^2+86x+150=0 equation: 


Simplifying
8x2 + 86x + 150 = 0

Reorder the terms:
150 + 86x + 8x2 = 0

Solving
150 + 86x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(75 + 43x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(75 + 43x + 4x2)' equal to zero and attempt to solve:

Simplifying
75 + 43x + 4x2 = 0

Solving
75 + 43x + 4x2 = 0

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

Divide each side by '4'.
18.75 + 10.75x + x2 = 0

Move the constant term to the right:

Add '-18.75' to each side of the equation.
18.75 + 10.75x + -18.75 + x2 = 0 + -18.75

Reorder the terms:
18.75 + -18.75 + 10.75x + x2 = 0 + -18.75

Combine like terms: 18.75 + -18.75 = 0.00
0.00 + 10.75x + x2 = 0 + -18.75
10.75x + x2 = 0 + -18.75

Combine like terms: 0 + -18.75 = -18.75
10.75x + x2 = -18.75

The x term is 10.75x.  Take half its coefficient (5.375).
Square it (28.890625) and add it to both sides.

Add '28.890625' to each side of the equation.
10.75x + 28.890625 + x2 = -18.75 + 28.890625

Reorder the terms:
28.890625 + 10.75x + x2 = -18.75 + 28.890625

Combine like terms: -18.75 + 28.890625 = 10.140625
28.890625 + 10.75x + x2 = 10.140625

Factor a perfect square on the left side:
(x + 5.375)(x + 5.375) = 10.140625

Calculate the square root of the right side: 3.184434801

Break this problem into two subproblems by setting 
(x + 5.375) equal to 3.184434801 and -3.184434801.


Subproblem 1
x + 5.375 = 3.184434801

Simplifying
x + 5.375 = 3.184434801

Reorder the terms:
5.375 + x = 3.184434801

Solving
5.375 + x = 3.184434801

Solving for variable 'x'.

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

Add '-5.375' to each side of the equation.
5.375 + -5.375 + x = 3.184434801 + -5.375

Combine like terms: 5.375 + -5.375 = 0.000
0.000 + x = 3.184434801 + -5.375
x = 3.184434801 + -5.375

Combine like terms: 3.184434801 + -5.375 = -2.190565199
x = -2.190565199

Simplifying
x = -2.190565199


Subproblem 2
x + 5.375 = -3.184434801

Simplifying
x + 5.375 = -3.184434801

Reorder the terms:
5.375 + x = -3.184434801

Solving
5.375 + x = -3.184434801

Solving for variable 'x'.

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

Add '-5.375' to each side of the equation.
5.375 + -5.375 + x = -3.184434801 + -5.375

Combine like terms: 5.375 + -5.375 = 0.000
0.000 + x = -3.184434801 + -5.375
x = -3.184434801 + -5.375

Combine like terms: -3.184434801 + -5.375 = -8.559434801
x = -8.559434801

Simplifying
x = -8.559434801


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.190565199, -8.559434801}
Solution
x = {-2.190565199, -8.559434801}

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