X^2-90X+450=0

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Solution for X^2-90X+450=0 equation:


Simplifying
X2 + -90X + 450 = 0

Reorder the terms:
450 + -90X + X2 = 0

Solving
450 + -90X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-450' to each side of the equation.
450 + -90X + -450 + X2 = 0 + -450

Reorder the terms:
450 + -450 + -90X + X2 = 0 + -450

Combine like terms: 450 + -450 = 0
0 + -90X + X2 = 0 + -450
-90X + X2 = 0 + -450

Combine like terms: 0 + -450 = -450
-90X + X2 = -450

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 = -450 + 2025

Reorder the terms:
2025 + -90X + X2 = -450 + 2025

Combine like terms: -450 + 2025 = 1575
2025 + -90X + X2 = 1575

Factor a perfect square on the left side:
(X + -45)(X + -45) = 1575

Calculate the square root of the right side: 39.686269666

Break this problem into two subproblems by setting 
(X + -45) equal to 39.686269666 and -39.686269666.

Subproblem 1

X + -45 = 39.686269666 Simplifying X + -45 = 39.686269666 Reorder the terms: -45 + X = 39.686269666 Solving -45 + X = 39.686269666 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 = 39.686269666 + 45 Combine like terms: -45 + 45 = 0 0 + X = 39.686269666 + 45 X = 39.686269666 + 45 Combine like terms: 39.686269666 + 45 = 84.686269666 X = 84.686269666 Simplifying X = 84.686269666

Subproblem 2

X + -45 = -39.686269666 Simplifying X + -45 = -39.686269666 Reorder the terms: -45 + X = -39.686269666 Solving -45 + X = -39.686269666 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 = -39.686269666 + 45 Combine like terms: -45 + 45 = 0 0 + X = -39.686269666 + 45 X = -39.686269666 + 45 Combine like terms: -39.686269666 + 45 = 5.313730334 X = 5.313730334 Simplifying X = 5.313730334

Solution

The solution to the problem is based on the solutions from the subproblems. X = {84.686269666, 5.313730334}

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