5x^2-30x+20=0

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Solution for 5x^2-30x+20=0 equation: 


Simplifying
5x2 + -30x + 20 = 0

Reorder the terms:
20 + -30x + 5x2 = 0

Solving
20 + -30x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + -6x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(4 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
4 + -6x + x2 = 0

Solving
4 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -6x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -6x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -6x + x2 = 0 + -4
-6x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-6x + x2 = -4

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 = -4 + 9

Reorder the terms:
9 + -6x + x2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + -6x + x2 = 5

Factor a perfect square on the left side:
(x + -3)(x + -3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -3) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + -3 = 2.236067978

Simplifying
x + -3 = 2.236067978

Reorder the terms:
-3 + x = 2.236067978

Solving
-3 + x = 2.236067978

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 = 2.236067978 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.236067978 + 3
x = 2.236067978 + 3

Combine like terms: 2.236067978 + 3 = 5.236067978
x = 5.236067978

Simplifying
x = 5.236067978


Subproblem 2
x + -3 = -2.236067978

Simplifying
x + -3 = -2.236067978

Reorder the terms:
-3 + x = -2.236067978

Solving
-3 + x = -2.236067978

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 = -2.236067978 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.236067978 + 3
x = -2.236067978 + 3

Combine like terms: -2.236067978 + 3 = 0.763932022
x = 0.763932022

Simplifying
x = 0.763932022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.236067978, 0.763932022}
Solution
x = {5.236067978, 0.763932022}

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