2x^2-60x+300=0

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Solution for 2x^2-60x+300=0 equation: 


Simplifying
2x2 + -60x + 300 = 0

Reorder the terms:
300 + -60x + 2x2 = 0

Solving
300 + -60x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(150 + -30x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(150 + -30x + x2)' equal to zero and attempt to solve:

Simplifying
150 + -30x + x2 = 0

Solving
150 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-150' to each side of the equation.
150 + -30x + -150 + x2 = 0 + -150

Reorder the terms:
150 + -150 + -30x + x2 = 0 + -150

Combine like terms: 150 + -150 = 0
0 + -30x + x2 = 0 + -150
-30x + x2 = 0 + -150

Combine like terms: 0 + -150 = -150
-30x + x2 = -150

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 = -150 + 225

Reorder the terms:
225 + -30x + x2 = -150 + 225

Combine like terms: -150 + 225 = 75
225 + -30x + x2 = 75

Factor a perfect square on the left side:
(x + -15)(x + -15) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + -15) equal to 8.660254038 and -8.660254038.


Subproblem 1
x + -15 = 8.660254038

Simplifying
x + -15 = 8.660254038

Reorder the terms:
-15 + x = 8.660254038

Solving
-15 + x = 8.660254038

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 = 8.660254038 + 15

Combine like terms: -15 + 15 = 0
0 + x = 8.660254038 + 15
x = 8.660254038 + 15

Combine like terms: 8.660254038 + 15 = 23.660254038
x = 23.660254038

Simplifying
x = 23.660254038


Subproblem 2
x + -15 = -8.660254038

Simplifying
x + -15 = -8.660254038

Reorder the terms:
-15 + x = -8.660254038

Solving
-15 + x = -8.660254038

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 = -8.660254038 + 15

Combine like terms: -15 + 15 = 0
0 + x = -8.660254038 + 15
x = -8.660254038 + 15

Combine like terms: -8.660254038 + 15 = 6.339745962
x = 6.339745962

Simplifying
x = 6.339745962


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.660254038, 6.339745962}
Solution
x = {23.660254038, 6.339745962}

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