2x^2-60x+36=0

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Solution for 2x^2-60x+36=0 equation: 


Simplifying
2x2 + -60x + 36 = 0

Reorder the terms:
36 + -60x + 2x2 = 0

Solving
36 + -60x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -30x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(18 + -30x + x2)' equal to zero and attempt to solve:

Simplifying
18 + -30x + x2 = 0

Solving
18 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -30x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -30x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -30x + x2 = 0 + -18
-30x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-30x + x2 = -18

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -18 + 225

Reorder the terms:
225 + -30x + x2 = -18 + 225

Combine like terms: -18 + 225 = 207
225 + -30x + x2 = 207

Factor a perfect square on the left side:
(x + -15)(x + -15) = 207

Calculate the square root of the right side: 14.38749457

Break this problem into two subproblems by setting 
(x + -15) equal to 14.38749457 and -14.38749457.


Subproblem 1
x + -15 = 14.38749457

Simplifying
x + -15 = 14.38749457

Reorder the terms:
-15 + x = 14.38749457

Solving
-15 + x = 14.38749457

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 14.38749457 + 15

Combine like terms: -15 + 15 = 0
0 + x = 14.38749457 + 15
x = 14.38749457 + 15

Combine like terms: 14.38749457 + 15 = 29.38749457
x = 29.38749457

Simplifying
x = 29.38749457


Subproblem 2
x + -15 = -14.38749457

Simplifying
x + -15 = -14.38749457

Reorder the terms:
-15 + x = -14.38749457

Solving
-15 + x = -14.38749457

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -14.38749457 + 15

Combine like terms: -15 + 15 = 0
0 + x = -14.38749457 + 15
x = -14.38749457 + 15

Combine like terms: -14.38749457 + 15 = 0.61250543
x = 0.61250543

Simplifying
x = 0.61250543


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.38749457, 0.61250543}
Solution
x = {29.38749457, 0.61250543}

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