x^2-90x+225=0

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Solution for x^2-90x+225=0 equation:


Simplifying
x2 + -90x + 225 = 0

Reorder the terms:
225 + -90x + x2 = 0

Solving
225 + -90x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-225' to each side of the equation.
225 + -90x + -225 + x2 = 0 + -225

Reorder the terms:
225 + -225 + -90x + x2 = 0 + -225

Combine like terms: 225 + -225 = 0
0 + -90x + x2 = 0 + -225
-90x + x2 = 0 + -225

Combine like terms: 0 + -225 = -225
-90x + x2 = -225

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 = -225 + 2025

Reorder the terms:
2025 + -90x + x2 = -225 + 2025

Combine like terms: -225 + 2025 = 1800
2025 + -90x + x2 = 1800

Factor a perfect square on the left side:
(x + -45)(x + -45) = 1800

Calculate the square root of the right side: 42.426406871

Break this problem into two subproblems by setting 
(x + -45) equal to 42.426406871 and -42.426406871.

Subproblem 1

x + -45 = 42.426406871 Simplifying x + -45 = 42.426406871 Reorder the terms: -45 + x = 42.426406871 Solving -45 + x = 42.426406871 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 = 42.426406871 + 45 Combine like terms: -45 + 45 = 0 0 + x = 42.426406871 + 45 x = 42.426406871 + 45 Combine like terms: 42.426406871 + 45 = 87.426406871 x = 87.426406871 Simplifying x = 87.426406871

Subproblem 2

x + -45 = -42.426406871 Simplifying x + -45 = -42.426406871 Reorder the terms: -45 + x = -42.426406871 Solving -45 + x = -42.426406871 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 = -42.426406871 + 45 Combine like terms: -45 + 45 = 0 0 + x = -42.426406871 + 45 x = -42.426406871 + 45 Combine like terms: -42.426406871 + 45 = 2.573593129 x = 2.573593129 Simplifying x = 2.573593129

Solution

The solution to the problem is based on the solutions from the subproblems. x = {87.426406871, 2.573593129}

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