5x^2-80x+400=130

Solution for 5x^2-80x+400=130 equation:

Simplifying
5x2 + -80x + 400 = 130

Reorder the terms:
400 + -80x + 5x2 = 130

Solving
400 + -80x + 5x2 = 130

Solving for variable 'x'.

Reorder the terms:
400 + -130 + -80x + 5x2 = 130 + -130

Combine like terms: 400 + -130 = 270
270 + -80x + 5x2 = 130 + -130

Combine like terms: 130 + -130 = 0
270 + -80x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(54 + -16x + x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(54 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
54 + -16x + x2 = 0

Solving
54 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + -16x + -54 + x2 = 0 + -54

Reorder the terms:
54 + -54 + -16x + x2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -16x + x2 = 0 + -54
-16x + x2 = 0 + -54

Combine like terms: 0 + -54 = -54
-16x + x2 = -54

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -54 + 64

Reorder the terms:
64 + -16x + x2 = -54 + 64

Combine like terms: -54 + 64 = 10
64 + -16x + x2 = 10

Factor a perfect square on the left side:
(x + -8)(x + -8) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -8) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + -8 = 3.16227766

Simplifying
x + -8 = 3.16227766

Reorder the terms:
-8 + x = 3.16227766

Solving
-8 + x = 3.16227766

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 3.16227766 + 8

Combine like terms: -8 + 8 = 0
0 + x = 3.16227766 + 8
x = 3.16227766 + 8

Combine like terms: 3.16227766 + 8 = 11.16227766
x = 11.16227766

Simplifying
x = 11.16227766

Subproblem 2
x + -8 = -3.16227766

Simplifying
x + -8 = -3.16227766

Reorder the terms:
-8 + x = -3.16227766

Solving
-8 + x = -3.16227766

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -3.16227766 + 8

Combine like terms: -8 + 8 = 0
0 + x = -3.16227766 + 8
x = -3.16227766 + 8

Combine like terms: -3.16227766 + 8 = 4.83772234
x = 4.83772234

Simplifying
x = 4.83772234

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.16227766, 4.83772234}
Solution
x = {11.16227766, 4.83772234}