x^2-30x-75=0

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Solution for x^2-30x-75=0 equation: 


Simplifying
x2 + -30x + -75 = 0

Reorder the terms:
-75 + -30x + x2 = 0

Solving
-75 + -30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + -30x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + -30x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -30x + x2 = 0 + 75
-30x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
-30x + x2 = 75

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 = 75 + 225

Reorder the terms:
225 + -30x + x2 = 75 + 225

Combine like terms: 75 + 225 = 300
225 + -30x + x2 = 300

Factor a perfect square on the left side:
(x + -15)(x + -15) = 300

Calculate the square root of the right side: 17.320508076

Break this problem into two subproblems by setting 
(x + -15) equal to 17.320508076 and -17.320508076.


Subproblem 1
x + -15 = 17.320508076

Simplifying
x + -15 = 17.320508076

Reorder the terms:
-15 + x = 17.320508076

Solving
-15 + x = 17.320508076

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 = 17.320508076 + 15

Combine like terms: -15 + 15 = 0
0 + x = 17.320508076 + 15
x = 17.320508076 + 15

Combine like terms: 17.320508076 + 15 = 32.320508076
x = 32.320508076

Simplifying
x = 32.320508076


Subproblem 2
x + -15 = -17.320508076

Simplifying
x + -15 = -17.320508076

Reorder the terms:
-15 + x = -17.320508076

Solving
-15 + x = -17.320508076

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 = -17.320508076 + 15

Combine like terms: -15 + 15 = 0
0 + x = -17.320508076 + 15
x = -17.320508076 + 15

Combine like terms: -17.320508076 + 15 = -2.320508076
x = -2.320508076

Simplifying
x = -2.320508076


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.320508076, -2.320508076}

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