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Simplifying 200 = 0.008x2 + 0.518x + 131.886 Reorder the terms: 200 = 131.886 + 0.518x + 0.008x2 Solving 200 = 131.886 + 0.518x + 0.008x2 Solving for variable 'x'. Combine like terms: 200 + -131.886 = 68.114 68.114 + -0.518x + -0.008x2 = 131.886 + 0.518x + 0.008x2 + -131.886 + -0.518x + -0.008x2 Reorder the terms: 68.114 + -0.518x + -0.008x2 = 131.886 + -131.886 + 0.518x + -0.518x + 0.008x2 + -0.008x2 Combine like terms: 131.886 + -131.886 = 0.000 68.114 + -0.518x + -0.008x2 = 0.000 + 0.518x + -0.518x + 0.008x2 + -0.008x2 68.114 + -0.518x + -0.008x2 = 0.518x + -0.518x + 0.008x2 + -0.008x2 Combine like terms: 0.518x + -0.518x = 0.000 68.114 + -0.518x + -0.008x2 = 0.000 + 0.008x2 + -0.008x2 68.114 + -0.518x + -0.008x2 = 0.008x2 + -0.008x2 Combine like terms: 0.008x2 + -0.008x2 = 0.000 68.114 + -0.518x + -0.008x2 = 0.000 Begin completing the square. Divide all terms by -0.008 the coefficient of the squared term: Divide each side by '-0.008'. -8514.25 + 64.75x + x2 = 0 Move the constant term to the right: Add '8514.25' to each side of the equation. -8514.25 + 64.75x + 8514.25 + x2 = 0 + 8514.25 Reorder the terms: -8514.25 + 8514.25 + 64.75x + x2 = 0 + 8514.25 Combine like terms: -8514.25 + 8514.25 = 0.00 0.00 + 64.75x + x2 = 0 + 8514.25 64.75x + x2 = 0 + 8514.25 Combine like terms: 0 + 8514.25 = 8514.25 64.75x + x2 = 8514.25 The x term is 64.75x. Take half its coefficient (32.375). Square it (1048.140625) and add it to both sides. Add '1048.140625' to each side of the equation. 64.75x + 1048.140625 + x2 = 8514.25 + 1048.140625 Reorder the terms: 1048.140625 + 64.75x + x2 = 8514.25 + 1048.140625 Combine like terms: 8514.25 + 1048.140625 = 9562.390625 1048.140625 + 64.75x + x2 = 9562.390625 Factor a perfect square on the left side: (x + 32.375)(x + 32.375) = 9562.390625 Calculate the square root of the right side: 97.787476831 Break this problem into two subproblems by setting (x + 32.375) equal to 97.787476831 and -97.787476831.Subproblem 1
x + 32.375 = 97.787476831 Simplifying x + 32.375 = 97.787476831 Reorder the terms: 32.375 + x = 97.787476831 Solving 32.375 + x = 97.787476831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32.375' to each side of the equation. 32.375 + -32.375 + x = 97.787476831 + -32.375 Combine like terms: 32.375 + -32.375 = 0.000 0.000 + x = 97.787476831 + -32.375 x = 97.787476831 + -32.375 Combine like terms: 97.787476831 + -32.375 = 65.412476831 x = 65.412476831 Simplifying x = 65.412476831Subproblem 2
x + 32.375 = -97.787476831 Simplifying x + 32.375 = -97.787476831 Reorder the terms: 32.375 + x = -97.787476831 Solving 32.375 + x = -97.787476831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32.375' to each side of the equation. 32.375 + -32.375 + x = -97.787476831 + -32.375 Combine like terms: 32.375 + -32.375 = 0.000 0.000 + x = -97.787476831 + -32.375 x = -97.787476831 + -32.375 Combine like terms: -97.787476831 + -32.375 = -130.162476831 x = -130.162476831 Simplifying x = -130.162476831Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.412476831, -130.162476831}
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