4x^2-140x+489=0

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Solution for 4x^2-140x+489=0 equation: 


Simplifying
4x2 + -140x + 489 = 0

Reorder the terms:
489 + -140x + 4x2 = 0

Solving
489 + -140x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
122.25 + -35x + x2 = 0

Move the constant term to the right:

Add '-122.25' to each side of the equation.
122.25 + -35x + -122.25 + x2 = 0 + -122.25

Reorder the terms:
122.25 + -122.25 + -35x + x2 = 0 + -122.25

Combine like terms: 122.25 + -122.25 = 0.00
0.00 + -35x + x2 = 0 + -122.25
-35x + x2 = 0 + -122.25

Combine like terms: 0 + -122.25 = -122.25
-35x + x2 = -122.25

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = -122.25 + 306.25

Reorder the terms:
306.25 + -35x + x2 = -122.25 + 306.25

Combine like terms: -122.25 + 306.25 = 184
306.25 + -35x + x2 = 184

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 184

Calculate the square root of the right side: 13.564659966

Break this problem into two subproblems by setting 
(x + -17.5) equal to 13.564659966 and -13.564659966.


Subproblem 1
x + -17.5 = 13.564659966

Simplifying
x + -17.5 = 13.564659966

Reorder the terms:
-17.5 + x = 13.564659966

Solving
-17.5 + x = 13.564659966

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 13.564659966 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 13.564659966 + 17.5
x = 13.564659966 + 17.5

Combine like terms: 13.564659966 + 17.5 = 31.064659966
x = 31.064659966

Simplifying
x = 31.064659966


Subproblem 2
x + -17.5 = -13.564659966

Simplifying
x + -17.5 = -13.564659966

Reorder the terms:
-17.5 + x = -13.564659966

Solving
-17.5 + x = -13.564659966

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -13.564659966 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -13.564659966 + 17.5
x = -13.564659966 + 17.5

Combine like terms: -13.564659966 + 17.5 = 3.935340034
x = 3.935340034

Simplifying
x = 3.935340034


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.064659966, 3.935340034}

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