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Simplifying (20 + -0.5x)(3 + -0.1x) = 0 Multiply (20 + -0.5x) * (3 + -0.1x) (20(3 + -0.1x) + -0.5x * (3 + -0.1x)) = 0 ((3 * 20 + -0.1x * 20) + -0.5x * (3 + -0.1x)) = 0 ((60 + -2x) + -0.5x * (3 + -0.1x)) = 0 (60 + -2x + (3 * -0.5x + -0.1x * -0.5x)) = 0 (60 + -2x + (-1.5x + 0.05x2)) = 0 Combine like terms: -2x + -1.5x = -3.5x (60 + -3.5x + 0.05x2) = 0 Solving 60 + -3.5x + 0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 1200 + -70x + x2 = 0 Move the constant term to the right: Add '-1200' to each side of the equation. 1200 + -70x + -1200 + x2 = 0 + -1200 Reorder the terms: 1200 + -1200 + -70x + x2 = 0 + -1200 Combine like terms: 1200 + -1200 = 0 0 + -70x + x2 = 0 + -1200 -70x + x2 = 0 + -1200 Combine like terms: 0 + -1200 = -1200 -70x + x2 = -1200 The x term is -70x. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70x + 1225 + x2 = -1200 + 1225 Reorder the terms: 1225 + -70x + x2 = -1200 + 1225 Combine like terms: -1200 + 1225 = 25 1225 + -70x + x2 = 25 Factor a perfect square on the left side: (x + -35)(x + -35) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + -35) equal to 5 and -5.Subproblem 1
x + -35 = 5 Simplifying x + -35 = 5 Reorder the terms: -35 + x = 5 Solving -35 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 5 + 35 Combine like terms: -35 + 35 = 0 0 + x = 5 + 35 x = 5 + 35 Combine like terms: 5 + 35 = 40 x = 40 Simplifying x = 40Subproblem 2
x + -35 = -5 Simplifying x + -35 = -5 Reorder the terms: -35 + x = -5 Solving -35 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -5 + 35 Combine like terms: -35 + 35 = 0 0 + x = -5 + 35 x = -5 + 35 Combine like terms: -5 + 35 = 30 x = 30 Simplifying x = 30Solution
The solution to the problem is based on the solutions from the subproblems. x = {40, 30}
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