5x^2-80x+150=0

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Solution for 5x^2-80x+150=0 equation: 


Simplifying
5x2 + -80x + 150 = 0

Reorder the terms:
150 + -80x + 5x2 = 0

Solving
150 + -80x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(30 + -16x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(30 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
30 + -16x + x2 = 0

Solving
30 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -16x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + -16x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -16x + x2 = 0 + -30
-16x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
-16x + x2 = -30

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 = -30 + 64

Reorder the terms:
64 + -16x + x2 = -30 + 64

Combine like terms: -30 + 64 = 34
64 + -16x + x2 = 34

Factor a perfect square on the left side:
(x + -8)(x + -8) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + -8) equal to 5.830951895 and -5.830951895.


Subproblem 1
x + -8 = 5.830951895

Simplifying
x + -8 = 5.830951895

Reorder the terms:
-8 + x = 5.830951895

Solving
-8 + x = 5.830951895

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 = 5.830951895 + 8

Combine like terms: -8 + 8 = 0
0 + x = 5.830951895 + 8
x = 5.830951895 + 8

Combine like terms: 5.830951895 + 8 = 13.830951895
x = 13.830951895

Simplifying
x = 13.830951895


Subproblem 2
x + -8 = -5.830951895

Simplifying
x + -8 = -5.830951895

Reorder the terms:
-8 + x = -5.830951895

Solving
-8 + x = -5.830951895

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 = -5.830951895 + 8

Combine like terms: -8 + 8 = 0
0 + x = -5.830951895 + 8
x = -5.830951895 + 8

Combine like terms: -5.830951895 + 8 = 2.169048105
x = 2.169048105

Simplifying
x = 2.169048105


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.830951895, 2.169048105}
Solution
x = {13.830951895, 2.169048105}

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