100=18x-.5x^2

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Solution for 100=18x-.5x^2 equation:


Simplifying
100 = 18x + -0.5x2

Solving
100 = 18x + -0.5x2

Solving for variable 'x'.

Reorder the terms:
100 + -18x + 0.5x2 = 18x + -18x + -0.5x2 + 0.5x2

Combine like terms: 18x + -18x = 0
100 + -18x + 0.5x2 = 0 + -0.5x2 + 0.5x2
100 + -18x + 0.5x2 = -0.5x2 + 0.5x2

Combine like terms: -0.5x2 + 0.5x2 = 0.0
100 + -18x + 0.5x2 = 0.0

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

Divide each side by '0.5'.
200 + -36x + x2 = 0

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + -36x + -200 + x2 = 0 + -200

Reorder the terms:
200 + -200 + -36x + x2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -36x + x2 = 0 + -200
-36x + x2 = 0 + -200

Combine like terms: 0 + -200 = -200
-36x + x2 = -200

The x term is -36x.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36x + 324 + x2 = -200 + 324

Reorder the terms:
324 + -36x + x2 = -200 + 324

Combine like terms: -200 + 324 = 124
324 + -36x + x2 = 124

Factor a perfect square on the left side:
(x + -18)(x + -18) = 124

Calculate the square root of the right side: 11.135528726

Break this problem into two subproblems by setting 
(x + -18) equal to 11.135528726 and -11.135528726.

Subproblem 1

x + -18 = 11.135528726 Simplifying x + -18 = 11.135528726 Reorder the terms: -18 + x = 11.135528726 Solving -18 + x = 11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 11.135528726 + 18 Combine like terms: -18 + 18 = 0 0 + x = 11.135528726 + 18 x = 11.135528726 + 18 Combine like terms: 11.135528726 + 18 = 29.135528726 x = 29.135528726 Simplifying x = 29.135528726

Subproblem 2

x + -18 = -11.135528726 Simplifying x + -18 = -11.135528726 Reorder the terms: -18 + x = -11.135528726 Solving -18 + x = -11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -11.135528726 + 18 Combine like terms: -18 + 18 = 0 0 + x = -11.135528726 + 18 x = -11.135528726 + 18 Combine like terms: -11.135528726 + 18 = 6.864471274 x = 6.864471274 Simplifying x = 6.864471274

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.135528726, 6.864471274}

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