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Simplifying -0.0006(x)(x + -200) = 5 Reorder the terms: -0.0006x(-200 + x) = 5 (-200 * -0.0006x + x * -0.0006x) = 5 (0.12x + -0.0006x2) = 5 Solving 0.12x + -0.0006x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 0.12x + -0.0006x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 0.12x + -0.0006x2 = 0 Begin completing the square. Divide all terms by -0.0006 the coefficient of the squared term: Divide each side by '-0.0006'. 8333.333333 + -200x + x2 = 0 Move the constant term to the right: Add '-8333.333333' to each side of the equation. 8333.333333 + -200x + -8333.333333 + x2 = 0 + -8333.333333 Reorder the terms: 8333.333333 + -8333.333333 + -200x + x2 = 0 + -8333.333333 Combine like terms: 8333.333333 + -8333.333333 = 0.000000 0.000000 + -200x + x2 = 0 + -8333.333333 -200x + x2 = 0 + -8333.333333 Combine like terms: 0 + -8333.333333 = -8333.333333 -200x + x2 = -8333.333333 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -8333.333333 + 10000 Reorder the terms: 10000 + -200x + x2 = -8333.333333 + 10000 Combine like terms: -8333.333333 + 10000 = 1666.666667 10000 + -200x + x2 = 1666.666667 Factor a perfect square on the left side: (x + -100)(x + -100) = 1666.666667 Calculate the square root of the right side: 40.82482905 Break this problem into two subproblems by setting (x + -100) equal to 40.82482905 and -40.82482905.Subproblem 1
x + -100 = 40.82482905 Simplifying x + -100 = 40.82482905 Reorder the terms: -100 + x = 40.82482905 Solving -100 + x = 40.82482905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 40.82482905 + 100 Combine like terms: -100 + 100 = 0 0 + x = 40.82482905 + 100 x = 40.82482905 + 100 Combine like terms: 40.82482905 + 100 = 140.82482905 x = 140.82482905 Simplifying x = 140.82482905Subproblem 2
x + -100 = -40.82482905 Simplifying x + -100 = -40.82482905 Reorder the terms: -100 + x = -40.82482905 Solving -100 + x = -40.82482905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -40.82482905 + 100 Combine like terms: -100 + 100 = 0 0 + x = -40.82482905 + 100 x = -40.82482905 + 100 Combine like terms: -40.82482905 + 100 = 59.17517095 x = 59.17517095 Simplifying x = 59.17517095Solution
The solution to the problem is based on the solutions from the subproblems. x = {140.82482905, 59.17517095}
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