9.9=-0.01x^2+0.25x+9.44

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Solution for 9.9=-0.01x^2+0.25x+9.44 equation:


Simplifying
9.9 = -0.01x2 + 0.25x + 9.44

Reorder the terms:
9.9 = 9.44 + 0.25x + -0.01x2

Solving
9.9 = 9.44 + 0.25x + -0.01x2

Solving for variable 'x'.

Combine like terms: 9.9 + -9.44 = 0.46
0.46 + -0.25x + 0.01x2 = 9.44 + 0.25x + -0.01x2 + -9.44 + -0.25x + 0.01x2

Reorder the terms:
0.46 + -0.25x + 0.01x2 = 9.44 + -9.44 + 0.25x + -0.25x + -0.01x2 + 0.01x2

Combine like terms: 9.44 + -9.44 = 0.00
0.46 + -0.25x + 0.01x2 = 0.00 + 0.25x + -0.25x + -0.01x2 + 0.01x2
0.46 + -0.25x + 0.01x2 = 0.25x + -0.25x + -0.01x2 + 0.01x2

Combine like terms: 0.25x + -0.25x = 0.00
0.46 + -0.25x + 0.01x2 = 0.00 + -0.01x2 + 0.01x2
0.46 + -0.25x + 0.01x2 = -0.01x2 + 0.01x2

Combine like terms: -0.01x2 + 0.01x2 = 0.00
0.46 + -0.25x + 0.01x2 = 0.00

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

Divide each side by '0.01'.
46 + -25x + x2 = 0

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + -25x + -46 + x2 = 0 + -46

Reorder the terms:
46 + -46 + -25x + x2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + -25x + x2 = 0 + -46
-25x + x2 = 0 + -46

Combine like terms: 0 + -46 = -46
-25x + x2 = -46

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = -46 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -46 + 156.25

Combine like terms: -46 + 156.25 = 110.25
156.25 + -25x + x2 = 110.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 110.25

Calculate the square root of the right side: 10.5

Break this problem into two subproblems by setting 
(x + -12.5) equal to 10.5 and -10.5.

Subproblem 1

x + -12.5 = 10.5 Simplifying x + -12.5 = 10.5 Reorder the terms: -12.5 + x = 10.5 Solving -12.5 + x = 10.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 10.5 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 10.5 + 12.5 x = 10.5 + 12.5 Combine like terms: 10.5 + 12.5 = 23 x = 23 Simplifying x = 23

Subproblem 2

x + -12.5 = -10.5 Simplifying x + -12.5 = -10.5 Reorder the terms: -12.5 + x = -10.5 Solving -12.5 + x = -10.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -10.5 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -10.5 + 12.5 x = -10.5 + 12.5 Combine like terms: -10.5 + 12.5 = 2 x = 2 Simplifying x = 2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23, 2}

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