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Simplifying (20 + -0.4x)(7 + -0.1x) = 0 Multiply (20 + -0.4x) * (7 + -0.1x) (20(7 + -0.1x) + -0.4x * (7 + -0.1x)) = 0 ((7 * 20 + -0.1x * 20) + -0.4x * (7 + -0.1x)) = 0 ((140 + -2x) + -0.4x * (7 + -0.1x)) = 0 (140 + -2x + (7 * -0.4x + -0.1x * -0.4x)) = 0 (140 + -2x + (-2.8x + 0.04x2)) = 0 Combine like terms: -2x + -2.8x = -4.8x (140 + -4.8x + 0.04x2) = 0 Solving 140 + -4.8x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 3500 + -120x + x2 = 0 Move the constant term to the right: Add '-3500' to each side of the equation. 3500 + -120x + -3500 + x2 = 0 + -3500 Reorder the terms: 3500 + -3500 + -120x + x2 = 0 + -3500 Combine like terms: 3500 + -3500 = 0 0 + -120x + x2 = 0 + -3500 -120x + x2 = 0 + -3500 Combine like terms: 0 + -3500 = -3500 -120x + x2 = -3500 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = -3500 + 3600 Reorder the terms: 3600 + -120x + x2 = -3500 + 3600 Combine like terms: -3500 + 3600 = 100 3600 + -120x + x2 = 100 Factor a perfect square on the left side: (x + -60)(x + -60) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (x + -60) equal to 10 and -10.Subproblem 1
x + -60 = 10 Simplifying x + -60 = 10 Reorder the terms: -60 + x = 10 Solving -60 + x = 10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 10 + 60 Combine like terms: -60 + 60 = 0 0 + x = 10 + 60 x = 10 + 60 Combine like terms: 10 + 60 = 70 x = 70 Simplifying x = 70Subproblem 2
x + -60 = -10 Simplifying x + -60 = -10 Reorder the terms: -60 + x = -10 Solving -60 + x = -10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -10 + 60 Combine like terms: -60 + 60 = 0 0 + x = -10 + 60 x = -10 + 60 Combine like terms: -10 + 60 = 50 x = 50 Simplifying x = 50Solution
The solution to the problem is based on the solutions from the subproblems. x = {70, 50}
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