x^2-90x-600=0

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Solution for x^2-90x-600=0 equation: 


Simplifying
x2 + -90x + -600 = 0

Reorder the terms:
-600 + -90x + x2 = 0

Solving
-600 + -90x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '600' to each side of the equation.
-600 + -90x + 600 + x2 = 0 + 600

Reorder the terms:
-600 + 600 + -90x + x2 = 0 + 600

Combine like terms: -600 + 600 = 0
0 + -90x + x2 = 0 + 600
-90x + x2 = 0 + 600

Combine like terms: 0 + 600 = 600
-90x + x2 = 600

The x term is -90x.  Take half its coefficient (-45).
Square it (2025) and add it to both sides.

Add '2025' to each side of the equation.
-90x + 2025 + x2 = 600 + 2025

Reorder the terms:
2025 + -90x + x2 = 600 + 2025

Combine like terms: 600 + 2025 = 2625
2025 + -90x + x2 = 2625

Factor a perfect square on the left side:
(x + -45)(x + -45) = 2625

Calculate the square root of the right side: 51.23475383

Break this problem into two subproblems by setting 
(x + -45) equal to 51.23475383 and -51.23475383.


Subproblem 1
x + -45 = 51.23475383

Simplifying
x + -45 = 51.23475383

Reorder the terms:
-45 + x = 51.23475383

Solving
-45 + x = 51.23475383

Solving for variable 'x'.

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

Add '45' to each side of the equation.
-45 + 45 + x = 51.23475383 + 45

Combine like terms: -45 + 45 = 0
0 + x = 51.23475383 + 45
x = 51.23475383 + 45

Combine like terms: 51.23475383 + 45 = 96.23475383
x = 96.23475383

Simplifying
x = 96.23475383


Subproblem 2
x + -45 = -51.23475383

Simplifying
x + -45 = -51.23475383

Reorder the terms:
-45 + x = -51.23475383

Solving
-45 + x = -51.23475383

Solving for variable 'x'.

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

Add '45' to each side of the equation.
-45 + 45 + x = -51.23475383 + 45

Combine like terms: -45 + 45 = 0
0 + x = -51.23475383 + 45
x = -51.23475383 + 45

Combine like terms: -51.23475383 + 45 = -6.23475383
x = -6.23475383

Simplifying
x = -6.23475383


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {96.23475383, -6.23475383}

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