x^2-30x+9=0

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Solution for x^2-30x+9=0 equation:


Simplifying
x2 + -30x + 9 = 0

Reorder the terms:
9 + -30x + x2 = 0

Solving
9 + -30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -30x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -30x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -30x + x2 = 0 + -9
-30x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-30x + x2 = -9

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 = -9 + 225

Reorder the terms:
225 + -30x + x2 = -9 + 225

Combine like terms: -9 + 225 = 216
225 + -30x + x2 = 216

Factor a perfect square on the left side:
(x + -15)(x + -15) = 216

Calculate the square root of the right side: 14.696938457

Break this problem into two subproblems by setting 
(x + -15) equal to 14.696938457 and -14.696938457.


Subproblem 1
x + -15 = 14.696938457

Simplifying
x + -15 = 14.696938457

Reorder the terms:
-15 + x = 14.696938457

Solving
-15 + x = 14.696938457

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 = 14.696938457 + 15

Combine like terms: -15 + 15 = 0
0 + x = 14.696938457 + 15
x = 14.696938457 + 15

Combine like terms: 14.696938457 + 15 = 29.696938457
x = 29.696938457

Simplifying
x = 29.696938457


Subproblem 2
x + -15 = -14.696938457

Simplifying
x + -15 = -14.696938457

Reorder the terms:
-15 + x = -14.696938457

Solving
-15 + x = -14.696938457

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 = -14.696938457 + 15

Combine like terms: -15 + 15 = 0
0 + x = -14.696938457 + 15
x = -14.696938457 + 15

Combine like terms: -14.696938457 + 15 = 0.303061543
x = 0.303061543

Simplifying
x = 0.303061543


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.696938457, 0.303061543}

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