(9-0.3x)(2-0.1x)=0

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Solution for (9-0.3x)(2-0.1x)=0 equation:


Simplifying
(9 + -0.3x)(2 + -0.1x) = 0

Multiply (9 + -0.3x) * (2 + -0.1x)
(9(2 + -0.1x) + -0.3x * (2 + -0.1x)) = 0
((2 * 9 + -0.1x * 9) + -0.3x * (2 + -0.1x)) = 0
((18 + -0.9x) + -0.3x * (2 + -0.1x)) = 0
(18 + -0.9x + (2 * -0.3x + -0.1x * -0.3x)) = 0
(18 + -0.9x + (-0.6x + 0.03x2)) = 0

Combine like terms: -0.9x + -0.6x = -1.5x
(18 + -1.5x + 0.03x2) = 0

Solving
18 + -1.5x + 0.03x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.03'.
600 + -50x + x2 = 0

Move the constant term to the right:

Add '-600' to each side of the equation.
600 + -50x + -600 + x2 = 0 + -600

Reorder the terms:
600 + -600 + -50x + x2 = 0 + -600

Combine like terms: 600 + -600 = 0
0 + -50x + x2 = 0 + -600
-50x + x2 = 0 + -600

Combine like terms: 0 + -600 = -600
-50x + x2 = -600

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = -600 + 625

Reorder the terms:
625 + -50x + x2 = -600 + 625

Combine like terms: -600 + 625 = 25
625 + -50x + x2 = 25

Factor a perfect square on the left side:
(x + -25)(x + -25) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + -25) equal to 5 and -5.

Subproblem 1

x + -25 = 5 Simplifying x + -25 = 5 Reorder the terms: -25 + x = 5 Solving -25 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 5 + 25 Combine like terms: -25 + 25 = 0 0 + x = 5 + 25 x = 5 + 25 Combine like terms: 5 + 25 = 30 x = 30 Simplifying x = 30

Subproblem 2

x + -25 = -5 Simplifying x + -25 = -5 Reorder the terms: -25 + x = -5 Solving -25 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -5 + 25 Combine like terms: -25 + 25 = 0 0 + x = -5 + 25 x = -5 + 25 Combine like terms: -5 + 25 = 20 x = 20 Simplifying x = 20

Solution

The solution to the problem is based on the solutions from the subproblems. x = {30, 20}

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