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Simplifying 200 = 0.04x2 + 1.1x Reorder the terms: 200 = 1.1x + 0.04x2 Solving 200 = 1.1x + 0.04x2 Solving for variable 'x'. Reorder the terms: 200 + -1.1x + -0.04x2 = 1.1x + -1.1x + 0.04x2 + -0.04x2 Combine like terms: 1.1x + -1.1x = 0.0 200 + -1.1x + -0.04x2 = 0.0 + 0.04x2 + -0.04x2 200 + -1.1x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 200 + -1.1x + -0.04x2 = 0.00 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -5000 + 27.5x + x2 = 0 Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 27.5x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 27.5x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 27.5x + x2 = 0 + 5000 27.5x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 27.5x + x2 = 5000 The x term is 27.5x. Take half its coefficient (13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. 27.5x + 189.0625 + x2 = 5000 + 189.0625 Reorder the terms: 189.0625 + 27.5x + x2 = 5000 + 189.0625 Combine like terms: 5000 + 189.0625 = 5189.0625 189.0625 + 27.5x + x2 = 5189.0625 Factor a perfect square on the left side: (x + 13.75)(x + 13.75) = 5189.0625 Calculate the square root of the right side: 72.035147671 Break this problem into two subproblems by setting (x + 13.75) equal to 72.035147671 and -72.035147671.Subproblem 1
x + 13.75 = 72.035147671 Simplifying x + 13.75 = 72.035147671 Reorder the terms: 13.75 + x = 72.035147671 Solving 13.75 + x = 72.035147671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = 72.035147671 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = 72.035147671 + -13.75 x = 72.035147671 + -13.75 Combine like terms: 72.035147671 + -13.75 = 58.285147671 x = 58.285147671 Simplifying x = 58.285147671Subproblem 2
x + 13.75 = -72.035147671 Simplifying x + 13.75 = -72.035147671 Reorder the terms: 13.75 + x = -72.035147671 Solving 13.75 + x = -72.035147671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = -72.035147671 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = -72.035147671 + -13.75 x = -72.035147671 + -13.75 Combine like terms: -72.035147671 + -13.75 = -85.785147671 x = -85.785147671 Simplifying x = -85.785147671Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.285147671, -85.785147671}
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