5x^2-18x+14=12x+39

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Solution for 5x^2-18x+14=12x+39 equation: 


Simplifying
5x2 + -18x + 14 = 12x + 39

Reorder the terms:
14 + -18x + 5x2 = 12x + 39

Reorder the terms:
14 + -18x + 5x2 = 39 + 12x

Solving
14 + -18x + 5x2 = 39 + 12x

Solving for variable 'x'.

Reorder the terms:
14 + -39 + -18x + -12x + 5x2 = 39 + 12x + -39 + -12x

Combine like terms: 14 + -39 = -25
-25 + -18x + -12x + 5x2 = 39 + 12x + -39 + -12x

Combine like terms: -18x + -12x = -30x
-25 + -30x + 5x2 = 39 + 12x + -39 + -12x

Reorder the terms:
-25 + -30x + 5x2 = 39 + -39 + 12x + -12x

Combine like terms: 39 + -39 = 0
-25 + -30x + 5x2 = 0 + 12x + -12x
-25 + -30x + 5x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-25 + -30x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + -6x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + -6x + x2 = 0

Solving
-5 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -6x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -6x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6x + x2 = 0 + 5
-6x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-6x + x2 = 5

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 = 5 + 9

Reorder the terms:
9 + -6x + x2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + -6x + x2 = 14

Factor a perfect square on the left side:
(x + -3)(x + -3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -3) equal to 3.741657387 and -3.741657387.


Subproblem 1
x + -3 = 3.741657387

Simplifying
x + -3 = 3.741657387

Reorder the terms:
-3 + x = 3.741657387

Solving
-3 + x = 3.741657387

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 = 3.741657387 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.741657387 + 3
x = 3.741657387 + 3

Combine like terms: 3.741657387 + 3 = 6.741657387
x = 6.741657387

Simplifying
x = 6.741657387


Subproblem 2
x + -3 = -3.741657387

Simplifying
x + -3 = -3.741657387

Reorder the terms:
-3 + x = -3.741657387

Solving
-3 + x = -3.741657387

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 = -3.741657387 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.741657387 + 3
x = -3.741657387 + 3

Combine like terms: -3.741657387 + 3 = -0.741657387
x = -0.741657387

Simplifying
x = -0.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.741657387, -0.741657387}
Solution
x = {6.741657387, -0.741657387}

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