5x^2-130x+120=0

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Solution for 5x^2-130x+120=0 equation: 


Simplifying
5x2 + -130x + 120 = 0

Reorder the terms:
120 + -130x + 5x2 = 0

Solving
120 + -130x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(24 + -26x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(24 + -26x + x2)' equal to zero and attempt to solve:

Simplifying
24 + -26x + x2 = 0

Solving
24 + -26x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -26x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -26x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -26x + x2 = 0 + -24
-26x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-26x + x2 = -24

The x term is -26x.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26x + 169 + x2 = -24 + 169

Reorder the terms:
169 + -26x + x2 = -24 + 169

Combine like terms: -24 + 169 = 145
169 + -26x + x2 = 145

Factor a perfect square on the left side:
(x + -13)(x + -13) = 145

Calculate the square root of the right side: 12.041594579

Break this problem into two subproblems by setting 
(x + -13) equal to 12.041594579 and -12.041594579.


Subproblem 1
x + -13 = 12.041594579

Simplifying
x + -13 = 12.041594579

Reorder the terms:
-13 + x = 12.041594579

Solving
-13 + x = 12.041594579

Solving for variable 'x'.

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

Add '13' to each side of the equation.
-13 + 13 + x = 12.041594579 + 13

Combine like terms: -13 + 13 = 0
0 + x = 12.041594579 + 13
x = 12.041594579 + 13

Combine like terms: 12.041594579 + 13 = 25.041594579
x = 25.041594579

Simplifying
x = 25.041594579


Subproblem 2
x + -13 = -12.041594579

Simplifying
x + -13 = -12.041594579

Reorder the terms:
-13 + x = -12.041594579

Solving
-13 + x = -12.041594579

Solving for variable 'x'.

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

Add '13' to each side of the equation.
-13 + 13 + x = -12.041594579 + 13

Combine like terms: -13 + 13 = 0
0 + x = -12.041594579 + 13
x = -12.041594579 + 13

Combine like terms: -12.041594579 + 13 = 0.958405421
x = 0.958405421

Simplifying
x = 0.958405421


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.041594579, 0.958405421}
Solution
x = {25.041594579, 0.958405421}

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