2x^2-24x+30=0

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Solution for 2x^2-24x+30=0 equation: 


Simplifying
2x2 + -24x + 30 = 0

Reorder the terms:
30 + -24x + 2x2 = 0

Solving
30 + -24x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -12x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
15 + -12x + x2 = 0

Solving
15 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -12x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -12x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -12x + x2 = 0 + -15
-12x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-12x + x2 = -15

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -15 + 36

Reorder the terms:
36 + -12x + x2 = -15 + 36

Combine like terms: -15 + 36 = 21
36 + -12x + x2 = 21

Factor a perfect square on the left side:
(x + -6)(x + -6) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + -6) equal to 4.582575695 and -4.582575695.


Subproblem 1
x + -6 = 4.582575695

Simplifying
x + -6 = 4.582575695

Reorder the terms:
-6 + x = 4.582575695

Solving
-6 + x = 4.582575695

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 4.582575695 + 6

Combine like terms: -6 + 6 = 0
0 + x = 4.582575695 + 6
x = 4.582575695 + 6

Combine like terms: 4.582575695 + 6 = 10.582575695
x = 10.582575695

Simplifying
x = 10.582575695


Subproblem 2
x + -6 = -4.582575695

Simplifying
x + -6 = -4.582575695

Reorder the terms:
-6 + x = -4.582575695

Solving
-6 + x = -4.582575695

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -4.582575695 + 6

Combine like terms: -6 + 6 = 0
0 + x = -4.582575695 + 6
x = -4.582575695 + 6

Combine like terms: -4.582575695 + 6 = 1.417424305
x = 1.417424305

Simplifying
x = 1.417424305


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.582575695, 1.417424305}
Solution
x = {10.582575695, 1.417424305}

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