6x^2-60x+90=0

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Solution for 6x^2-60x+90=0 equation: 


Simplifying
6x2 + -60x + 90 = 0

Reorder the terms:
90 + -60x + 6x2 = 0

Solving
90 + -60x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(15 + -10x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(15 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
15 + -10x + x2 = 0

Solving
15 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -10x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -10x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -10x + x2 = 0 + -15
-10x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-10x + x2 = -15

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -15 + 25

Reorder the terms:
25 + -10x + x2 = -15 + 25

Combine like terms: -15 + 25 = 10
25 + -10x + x2 = 10

Factor a perfect square on the left side:
(x + -5)(x + -5) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -5) equal to 3.16227766 and -3.16227766.


Subproblem 1
x + -5 = 3.16227766

Simplifying
x + -5 = 3.16227766

Reorder the terms:
-5 + x = 3.16227766

Solving
-5 + x = 3.16227766

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 3.16227766 + 5

Combine like terms: -5 + 5 = 0
0 + x = 3.16227766 + 5
x = 3.16227766 + 5

Combine like terms: 3.16227766 + 5 = 8.16227766
x = 8.16227766

Simplifying
x = 8.16227766


Subproblem 2
x + -5 = -3.16227766

Simplifying
x + -5 = -3.16227766

Reorder the terms:
-5 + x = -3.16227766

Solving
-5 + x = -3.16227766

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -3.16227766 + 5

Combine like terms: -5 + 5 = 0
0 + x = -3.16227766 + 5
x = -3.16227766 + 5

Combine like terms: -3.16227766 + 5 = 1.83772234
x = 1.83772234

Simplifying
x = 1.83772234


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.16227766, 1.83772234}
Solution
x = {8.16227766, 1.83772234}

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