6x^2+61x+60=0

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Solution for 6x^2+61x+60=0 equation: 


Simplifying
6x2 + 61x + 60 = 0

Reorder the terms:
60 + 61x + 6x2 = 0

Solving
60 + 61x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
10 + 10.16666667x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 10.16666667x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 10.16666667x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 10.16666667x + x2 = 0 + -10
10.16666667x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
10.16666667x + x2 = -10

The x term is 10.16666667x.  Take half its coefficient (5.083333335).
Square it (25.84027779) and add it to both sides.

Add '25.84027779' to each side of the equation.
10.16666667x + 25.84027779 + x2 = -10 + 25.84027779

Reorder the terms:
25.84027779 + 10.16666667x + x2 = -10 + 25.84027779

Combine like terms: -10 + 25.84027779 = 15.84027779
25.84027779 + 10.16666667x + x2 = 15.84027779

Factor a perfect square on the left side:
(x + 5.083333335)(x + 5.083333335) = 15.84027779

Calculate the square root of the right side: 3.979984647

Break this problem into two subproblems by setting 
(x + 5.083333335) equal to 3.979984647 and -3.979984647.


Subproblem 1
x + 5.083333335 = 3.979984647

Simplifying
x + 5.083333335 = 3.979984647

Reorder the terms:
5.083333335 + x = 3.979984647

Solving
5.083333335 + x = 3.979984647

Solving for variable 'x'.

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

Add '-5.083333335' to each side of the equation.
5.083333335 + -5.083333335 + x = 3.979984647 + -5.083333335

Combine like terms: 5.083333335 + -5.083333335 = 0.000000000
0.000000000 + x = 3.979984647 + -5.083333335
x = 3.979984647 + -5.083333335

Combine like terms: 3.979984647 + -5.083333335 = -1.103348688
x = -1.103348688

Simplifying
x = -1.103348688


Subproblem 2
x + 5.083333335 = -3.979984647

Simplifying
x + 5.083333335 = -3.979984647

Reorder the terms:
5.083333335 + x = -3.979984647

Solving
5.083333335 + x = -3.979984647

Solving for variable 'x'.

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

Add '-5.083333335' to each side of the equation.
5.083333335 + -5.083333335 + x = -3.979984647 + -5.083333335

Combine like terms: 5.083333335 + -5.083333335 = 0.000000000
0.000000000 + x = -3.979984647 + -5.083333335
x = -3.979984647 + -5.083333335

Combine like terms: -3.979984647 + -5.083333335 = -9.063317982
x = -9.063317982

Simplifying
x = -9.063317982


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.103348688, -9.063317982}

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