-0.5x^2+9x+20=

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Solution for -0.5x^2+9x+20= equation:


Simplifying
-0.5x2 + 9x + 20 = 0

Reorder the terms:
20 + 9x + -0.5x2 = 0

Solving
20 + 9x + -0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '-0.5'.
-40 + -18x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -18x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -18x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -18x + x2 = 0 + 40
-18x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-18x + x2 = 40

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 40 + 81

Reorder the terms:
81 + -18x + x2 = 40 + 81

Combine like terms: 40 + 81 = 121
81 + -18x + x2 = 121

Factor a perfect square on the left side:
(x + -9)(x + -9) = 121

Calculate the square root of the right side: 11

Break this problem into two subproblems by setting 
(x + -9) equal to 11 and -11.

Subproblem 1

x + -9 = 11 Simplifying x + -9 = 11 Reorder the terms: -9 + x = 11 Solving -9 + x = 11 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 11 + 9 Combine like terms: -9 + 9 = 0 0 + x = 11 + 9 x = 11 + 9 Combine like terms: 11 + 9 = 20 x = 20 Simplifying x = 20

Subproblem 2

x + -9 = -11 Simplifying x + -9 = -11 Reorder the terms: -9 + x = -11 Solving -9 + x = -11 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -11 + 9 Combine like terms: -9 + 9 = 0 0 + x = -11 + 9 x = -11 + 9 Combine like terms: -11 + 9 = -2 x = -2 Simplifying x = -2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20, -2}

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