5x^2-80x+14=0

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Solution for 5x^2-80x+14=0 equation: 


Simplifying
5x2 + -80x + 14 = 0

Reorder the terms:
14 + -80x + 5x2 = 0

Solving
14 + -80x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
2.8 + -16x + x2 = 0

Move the constant term to the right:

Add '-2.8' to each side of the equation.
2.8 + -16x + -2.8 + x2 = 0 + -2.8

Reorder the terms:
2.8 + -2.8 + -16x + x2 = 0 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + -16x + x2 = 0 + -2.8
-16x + x2 = 0 + -2.8

Combine like terms: 0 + -2.8 = -2.8
-16x + x2 = -2.8

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 = -2.8 + 64

Reorder the terms:
64 + -16x + x2 = -2.8 + 64

Combine like terms: -2.8 + 64 = 61.2
64 + -16x + x2 = 61.2

Factor a perfect square on the left side:
(x + -8)(x + -8) = 61.2

Calculate the square root of the right side: 7.823042886

Break this problem into two subproblems by setting 
(x + -8) equal to 7.823042886 and -7.823042886.


Subproblem 1
x + -8 = 7.823042886

Simplifying
x + -8 = 7.823042886

Reorder the terms:
-8 + x = 7.823042886

Solving
-8 + x = 7.823042886

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 = 7.823042886 + 8

Combine like terms: -8 + 8 = 0
0 + x = 7.823042886 + 8
x = 7.823042886 + 8

Combine like terms: 7.823042886 + 8 = 15.823042886
x = 15.823042886

Simplifying
x = 15.823042886


Subproblem 2
x + -8 = -7.823042886

Simplifying
x + -8 = -7.823042886

Reorder the terms:
-8 + x = -7.823042886

Solving
-8 + x = -7.823042886

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 = -7.823042886 + 8

Combine like terms: -8 + 8 = 0
0 + x = -7.823042886 + 8
x = -7.823042886 + 8

Combine like terms: -7.823042886 + 8 = 0.176957114
x = 0.176957114

Simplifying
x = 0.176957114


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.823042886, 0.176957114}

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