6x^2+54x-10=0

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Solution for 6x^2+54x-10=0 equation: 


Simplifying
6x2 + 54x + -10 = 0

Reorder the terms:
-10 + 54x + 6x2 = 0

Solving
-10 + 54x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 27x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 27x + 3x2)' equal to zero and attempt to solve:

Simplifying
-5 + 27x + 3x2 = 0

Solving
-5 + 27x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + 9x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 9x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 9x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 9x + x2 = 0 + 1.666666667
9x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
9x + x2 = 1.666666667

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 1.666666667 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 1.666666667 + 20.25

Combine like terms: 1.666666667 + 20.25 = 21.916666667
20.25 + 9x + x2 = 21.916666667

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 21.916666667

Calculate the square root of the right side: 4.681523968

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.681523968 and -4.681523968.


Subproblem 1
x + 4.5 = 4.681523968

Simplifying
x + 4.5 = 4.681523968

Reorder the terms:
4.5 + x = 4.681523968

Solving
4.5 + x = 4.681523968

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 4.681523968 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.681523968 + -4.5
x = 4.681523968 + -4.5

Combine like terms: 4.681523968 + -4.5 = 0.181523968
x = 0.181523968

Simplifying
x = 0.181523968


Subproblem 2
x + 4.5 = -4.681523968

Simplifying
x + 4.5 = -4.681523968

Reorder the terms:
4.5 + x = -4.681523968

Solving
4.5 + x = -4.681523968

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -4.681523968 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.681523968 + -4.5
x = -4.681523968 + -4.5

Combine like terms: -4.681523968 + -4.5 = -9.181523968
x = -9.181523968

Simplifying
x = -9.181523968


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.181523968, -9.181523968}
Solution
x = {0.181523968, -9.181523968}

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