x^2-30x+180=0

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Solution for x^2-30x+180=0 equation: 


Simplifying
x2 + -30x + 180 = 0

Reorder the terms:
180 + -30x + x2 = 0

Solving
180 + -30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-180' to each side of the equation.
180 + -30x + -180 + x2 = 0 + -180

Reorder the terms:
180 + -180 + -30x + x2 = 0 + -180

Combine like terms: 180 + -180 = 0
0 + -30x + x2 = 0 + -180
-30x + x2 = 0 + -180

Combine like terms: 0 + -180 = -180
-30x + x2 = -180

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -180 + 225

Reorder the terms:
225 + -30x + x2 = -180 + 225

Combine like terms: -180 + 225 = 45
225 + -30x + x2 = 45

Factor a perfect square on the left side:
(x + -15)(x + -15) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + -15) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + -15 = 6.708203933

Simplifying
x + -15 = 6.708203933

Reorder the terms:
-15 + x = 6.708203933

Solving
-15 + x = 6.708203933

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 6.708203933 + 15

Combine like terms: -15 + 15 = 0
0 + x = 6.708203933 + 15
x = 6.708203933 + 15

Combine like terms: 6.708203933 + 15 = 21.708203933
x = 21.708203933

Simplifying
x = 21.708203933


Subproblem 2
x + -15 = -6.708203933

Simplifying
x + -15 = -6.708203933

Reorder the terms:
-15 + x = -6.708203933

Solving
-15 + x = -6.708203933

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -6.708203933 + 15

Combine like terms: -15 + 15 = 0
0 + x = -6.708203933 + 15
x = -6.708203933 + 15

Combine like terms: -6.708203933 + 15 = 8.291796067
x = 8.291796067

Simplifying
x = 8.291796067


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.708203933, 8.291796067}

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