10x^2+60x+8=0

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Solution for 10x^2+60x+8=0 equation: 


Simplifying
10x2 + 60x + 8 = 0

Reorder the terms:
8 + 60x + 10x2 = 0

Solving
8 + 60x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 30x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 30x + 5x2)' equal to zero and attempt to solve:

Simplifying
4 + 30x + 5x2 = 0

Solving
4 + 30x + 5x2 = 0

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

Divide each side by '5'.
0.8 + 6x + x2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + 6x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + 6x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + 6x + x2 = 0 + -0.8
6x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
6x + x2 = -0.8

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -0.8 + 9

Reorder the terms:
9 + 6x + x2 = -0.8 + 9

Combine like terms: -0.8 + 9 = 8.2
9 + 6x + x2 = 8.2

Factor a perfect square on the left side:
(x + 3)(x + 3) = 8.2

Calculate the square root of the right side: 2.863564213

Break this problem into two subproblems by setting 
(x + 3) equal to 2.863564213 and -2.863564213.


Subproblem 1
x + 3 = 2.863564213

Simplifying
x + 3 = 2.863564213

Reorder the terms:
3 + x = 2.863564213

Solving
3 + x = 2.863564213

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2.863564213 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.863564213 + -3
x = 2.863564213 + -3

Combine like terms: 2.863564213 + -3 = -0.136435787
x = -0.136435787

Simplifying
x = -0.136435787


Subproblem 2
x + 3 = -2.863564213

Simplifying
x + 3 = -2.863564213

Reorder the terms:
3 + x = -2.863564213

Solving
3 + x = -2.863564213

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2.863564213 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.863564213 + -3
x = -2.863564213 + -3

Combine like terms: -2.863564213 + -3 = -5.863564213
x = -5.863564213

Simplifying
x = -5.863564213


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.136435787, -5.863564213}
Solution
x = {-0.136435787, -5.863564213}

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