-0.1x^2+18x-250=0

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Solution for -0.1x^2+18x-250=0 equation:


Simplifying
-0.1x2 + 18x + -250 = 0

Reorder the terms:
-250 + 18x + -0.1x2 = 0

Solving
-250 + 18x + -0.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-0.1'.
2500 + -180x + x2 = 0

Move the constant term to the right:

Add '-2500' to each side of the equation.
2500 + -180x + -2500 + x2 = 0 + -2500

Reorder the terms:
2500 + -2500 + -180x + x2 = 0 + -2500

Combine like terms: 2500 + -2500 = 0
0 + -180x + x2 = 0 + -2500
-180x + x2 = 0 + -2500

Combine like terms: 0 + -2500 = -2500
-180x + x2 = -2500

The x term is -180x.  Take half its coefficient (-90).
Square it (8100) and add it to both sides.

Add '8100' to each side of the equation.
-180x + 8100 + x2 = -2500 + 8100

Reorder the terms:
8100 + -180x + x2 = -2500 + 8100

Combine like terms: -2500 + 8100 = 5600
8100 + -180x + x2 = 5600

Factor a perfect square on the left side:
(x + -90)(x + -90) = 5600

Calculate the square root of the right side: 74.833147735

Break this problem into two subproblems by setting 
(x + -90) equal to 74.833147735 and -74.833147735.

Subproblem 1

x + -90 = 74.833147735 Simplifying x + -90 = 74.833147735 Reorder the terms: -90 + x = 74.833147735 Solving -90 + x = 74.833147735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 74.833147735 + 90 Combine like terms: -90 + 90 = 0 0 + x = 74.833147735 + 90 x = 74.833147735 + 90 Combine like terms: 74.833147735 + 90 = 164.833147735 x = 164.833147735 Simplifying x = 164.833147735

Subproblem 2

x + -90 = -74.833147735 Simplifying x + -90 = -74.833147735 Reorder the terms: -90 + x = -74.833147735 Solving -90 + x = -74.833147735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -74.833147735 + 90 Combine like terms: -90 + 90 = 0 0 + x = -74.833147735 + 90 x = -74.833147735 + 90 Combine like terms: -74.833147735 + 90 = 15.166852265 x = 15.166852265 Simplifying x = 15.166852265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {164.833147735, 15.166852265}

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