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Simplifying x(1 + -0.02x) = 10 (1 * x + -0.02x * x) = 10 (1x + -0.02x2) = 10 Solving 1x + -0.02x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 1x + -0.02x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 1x + -0.02x2 = 0 Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 500 + -50x + x2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -50x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -50x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -50x + x2 = 0 + -500 -50x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -50x + x2 = -500 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 = -500 + 625 Reorder the terms: 625 + -50x + x2 = -500 + 625 Combine like terms: -500 + 625 = 125 625 + -50x + x2 = 125 Factor a perfect square on the left side: (x + -25)(x + -25) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + -25) equal to 11.180339887 and -11.180339887.Subproblem 1
x + -25 = 11.180339887 Simplifying x + -25 = 11.180339887 Reorder the terms: -25 + x = 11.180339887 Solving -25 + x = 11.180339887 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 = 11.180339887 + 25 Combine like terms: -25 + 25 = 0 0 + x = 11.180339887 + 25 x = 11.180339887 + 25 Combine like terms: 11.180339887 + 25 = 36.180339887 x = 36.180339887 Simplifying x = 36.180339887Subproblem 2
x + -25 = -11.180339887 Simplifying x + -25 = -11.180339887 Reorder the terms: -25 + x = -11.180339887 Solving -25 + x = -11.180339887 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 = -11.180339887 + 25 Combine like terms: -25 + 25 = 0 0 + x = -11.180339887 + 25 x = -11.180339887 + 25 Combine like terms: -11.180339887 + 25 = 13.819660113 x = 13.819660113 Simplifying x = 13.819660113Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.180339887, 13.819660113}
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