0.1*x*x-3*x=9.9

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Solution for 0.1*x*x-3*x=9.9 equation:


Simplifying
0.1x * x + -3x = 9.9

Multiply x * x
0.1x2 + -3x = 9.9

Reorder the terms:
-3x + 0.1x2 = 9.9

Solving
-3x + 0.1x2 = 9.9

Solving for variable 'x'.

Reorder the terms:
-9.9 + -3x + 0.1x2 = 9.9 + -9.9

Combine like terms: 9.9 + -9.9 = 0.0
-9.9 + -3x + 0.1x2 = 0.0

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

Divide each side by '0.1'.
-99 + -30x + x2 = 0

Move the constant term to the right:

Add '99' to each side of the equation.
-99 + -30x + 99 + x2 = 0 + 99

Reorder the terms:
-99 + 99 + -30x + x2 = 0 + 99

Combine like terms: -99 + 99 = 0
0 + -30x + x2 = 0 + 99
-30x + x2 = 0 + 99

Combine like terms: 0 + 99 = 99
-30x + x2 = 99

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 99 + 225

Reorder the terms:
225 + -30x + x2 = 99 + 225

Combine like terms: 99 + 225 = 324
225 + -30x + x2 = 324

Factor a perfect square on the left side:
(x + -15)(x + -15) = 324

Calculate the square root of the right side: 18

Break this problem into two subproblems by setting 
(x + -15) equal to 18 and -18.

Subproblem 1

x + -15 = 18 Simplifying x + -15 = 18 Reorder the terms: -15 + x = 18 Solving -15 + x = 18 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 18 + 15 Combine like terms: -15 + 15 = 0 0 + x = 18 + 15 x = 18 + 15 Combine like terms: 18 + 15 = 33 x = 33 Simplifying x = 33

Subproblem 2

x + -15 = -18 Simplifying x + -15 = -18 Reorder the terms: -15 + x = -18 Solving -15 + x = -18 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -18 + 15 Combine like terms: -15 + 15 = 0 0 + x = -18 + 15 x = -18 + 15 Combine like terms: -18 + 15 = -3 x = -3 Simplifying x = -3

Solution

The solution to the problem is based on the solutions from the subproblems. x = {33, -3}

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