4x^2-90x+272=0

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Solution for 4x^2-90x+272=0 equation: 


Simplifying
4x2 + -90x + 272 = 0

Reorder the terms:
272 + -90x + 4x2 = 0

Solving
272 + -90x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(136 + -45x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(136 + -45x + 2x2)' equal to zero and attempt to solve:

Simplifying
136 + -45x + 2x2 = 0

Solving
136 + -45x + 2x2 = 0

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

Divide each side by '2'.
68 + -22.5x + x2 = 0

Move the constant term to the right:

Add '-68' to each side of the equation.
68 + -22.5x + -68 + x2 = 0 + -68

Reorder the terms:
68 + -68 + -22.5x + x2 = 0 + -68

Combine like terms: 68 + -68 = 0
0 + -22.5x + x2 = 0 + -68
-22.5x + x2 = 0 + -68

Combine like terms: 0 + -68 = -68
-22.5x + x2 = -68

The x term is -22.5x.  Take half its coefficient (-11.25).
Square it (126.5625) and add it to both sides.

Add '126.5625' to each side of the equation.
-22.5x + 126.5625 + x2 = -68 + 126.5625

Reorder the terms:
126.5625 + -22.5x + x2 = -68 + 126.5625

Combine like terms: -68 + 126.5625 = 58.5625
126.5625 + -22.5x + x2 = 58.5625

Factor a perfect square on the left side:
(x + -11.25)(x + -11.25) = 58.5625

Calculate the square root of the right side: 7.652613933

Break this problem into two subproblems by setting 
(x + -11.25) equal to 7.652613933 and -7.652613933.


Subproblem 1
x + -11.25 = 7.652613933

Simplifying
x + -11.25 = 7.652613933

Reorder the terms:
-11.25 + x = 7.652613933

Solving
-11.25 + x = 7.652613933

Solving for variable 'x'.

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

Add '11.25' to each side of the equation.
-11.25 + 11.25 + x = 7.652613933 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + x = 7.652613933 + 11.25
x = 7.652613933 + 11.25

Combine like terms: 7.652613933 + 11.25 = 18.902613933
x = 18.902613933

Simplifying
x = 18.902613933


Subproblem 2
x + -11.25 = -7.652613933

Simplifying
x + -11.25 = -7.652613933

Reorder the terms:
-11.25 + x = -7.652613933

Solving
-11.25 + x = -7.652613933

Solving for variable 'x'.

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

Add '11.25' to each side of the equation.
-11.25 + 11.25 + x = -7.652613933 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + x = -7.652613933 + 11.25
x = -7.652613933 + 11.25

Combine like terms: -7.652613933 + 11.25 = 3.597386067
x = 3.597386067

Simplifying
x = 3.597386067


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.902613933, 3.597386067}
Solution
x = {18.902613933, 3.597386067}

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