-0.1x^2+90x=20250

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Solution for -0.1x^2+90x=20250 equation:


Simplifying
-0.1x2 + 90x = 20250

Reorder the terms:
90x + -0.1x2 = 20250

Solving
90x + -0.1x2 = 20250

Solving for variable 'x'.

Reorder the terms:
-20250 + 90x + -0.1x2 = 20250 + -20250

Combine like terms: 20250 + -20250 = 0
-20250 + 90x + -0.1x2 = 0

Begin completing the square.  Divide all terms by
-0.1 the coefficient of the squared term: 

Divide each side by '-0.1'.
202500 + -900x + x2 = 0

Move the constant term to the right:

Add '-202500' to each side of the equation.
202500 + -900x + -202500 + x2 = 0 + -202500

Reorder the terms:
202500 + -202500 + -900x + x2 = 0 + -202500

Combine like terms: 202500 + -202500 = 0
0 + -900x + x2 = 0 + -202500
-900x + x2 = 0 + -202500

Combine like terms: 0 + -202500 = -202500
-900x + x2 = -202500

The x term is -900x.  Take half its coefficient (-450).
Square it (202500) and add it to both sides.

Add '202500' to each side of the equation.
-900x + 202500 + x2 = -202500 + 202500

Reorder the terms:
202500 + -900x + x2 = -202500 + 202500

Combine like terms: -202500 + 202500 = 0
202500 + -900x + x2 = 0

Factor a perfect square on the left side:
(x + -450)(x + -450) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(x + -450) equal to 0 and 0.

Subproblem 1

x + -450 = 0 Simplifying x + -450 = 0 Reorder the terms: -450 + x = 0 Solving -450 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + x = 0 + 450 Combine like terms: -450 + 450 = 0 0 + x = 0 + 450 x = 0 + 450 Combine like terms: 0 + 450 = 450 x = 450 Simplifying x = 450

Subproblem 2

x + -450 = 0 Simplifying x + -450 = 0 Reorder the terms: -450 + x = 0 Solving -450 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + x = 0 + 450 Combine like terms: -450 + 450 = 0 0 + x = 0 + 450 x = 0 + 450 Combine like terms: 0 + 450 = 450 x = 450 Simplifying x = 450

Solution

The solution to the problem is based on the solutions from the subproblems. x = {450, 450}

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