2x^2-18x+28=528

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Solution for 2x^2-18x+28=528 equation:


Simplifying
2x2 + -18x + 28 = 528

Reorder the terms:
28 + -18x + 2x2 = 528

Solving
28 + -18x + 2x2 = 528

Solving for variable 'x'.

Reorder the terms:
28 + -528 + -18x + 2x2 = 528 + -528

Combine like terms: 28 + -528 = -500
-500 + -18x + 2x2 = 528 + -528

Combine like terms: 528 + -528 = 0
-500 + -18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-250 + -9x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-250 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
-250 + -9x + x2 = 0

Solving
-250 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + -9x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + -9x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + -9x + x2 = 0 + 250
-9x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
-9x + x2 = 250

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 250 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 250 + 20.25

Combine like terms: 250 + 20.25 = 270.25
20.25 + -9x + x2 = 270.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 270.25

Calculate the square root of the right side: 16.439282223

Break this problem into two subproblems by setting 
(x + -4.5) equal to 16.439282223 and -16.439282223.


Subproblem 1
x + -4.5 = 16.439282223

Simplifying
x + -4.5 = 16.439282223

Reorder the terms:
-4.5 + x = 16.439282223

Solving
-4.5 + x = 16.439282223

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 16.439282223 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 16.439282223 + 4.5
x = 16.439282223 + 4.5

Combine like terms: 16.439282223 + 4.5 = 20.939282223
x = 20.939282223

Simplifying
x = 20.939282223


Subproblem 2
x + -4.5 = -16.439282223

Simplifying
x + -4.5 = -16.439282223

Reorder the terms:
-4.5 + x = -16.439282223

Solving
-4.5 + x = -16.439282223

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -16.439282223 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -16.439282223 + 4.5
x = -16.439282223 + 4.5

Combine like terms: -16.439282223 + 4.5 = -11.939282223
x = -11.939282223

Simplifying
x = -11.939282223


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.939282223, -11.939282223}
Solution
x = {20.939282223, -11.939282223}

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