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Simplifying 4 = 0.014x2 + -1.19x + 28.24 Reorder the terms: 4 = 28.24 + -1.19x + 0.014x2 Solving 4 = 28.24 + -1.19x + 0.014x2 Solving for variable 'x'. Combine like terms: 4 + -28.24 = -24.24 -24.24 + 1.19x + -0.014x2 = 28.24 + -1.19x + 0.014x2 + -28.24 + 1.19x + -0.014x2 Reorder the terms: -24.24 + 1.19x + -0.014x2 = 28.24 + -28.24 + -1.19x + 1.19x + 0.014x2 + -0.014x2 Combine like terms: 28.24 + -28.24 = 0.00 -24.24 + 1.19x + -0.014x2 = 0.00 + -1.19x + 1.19x + 0.014x2 + -0.014x2 -24.24 + 1.19x + -0.014x2 = -1.19x + 1.19x + 0.014x2 + -0.014x2 Combine like terms: -1.19x + 1.19x = 0.00 -24.24 + 1.19x + -0.014x2 = 0.00 + 0.014x2 + -0.014x2 -24.24 + 1.19x + -0.014x2 = 0.014x2 + -0.014x2 Combine like terms: 0.014x2 + -0.014x2 = 0.000 -24.24 + 1.19x + -0.014x2 = 0.000 Begin completing the square. Divide all terms by -0.014 the coefficient of the squared term: Divide each side by '-0.014'. 1731.428571 + -85x + x2 = 0 Move the constant term to the right: Add '-1731.428571' to each side of the equation. 1731.428571 + -85x + -1731.428571 + x2 = 0 + -1731.428571 Reorder the terms: 1731.428571 + -1731.428571 + -85x + x2 = 0 + -1731.428571 Combine like terms: 1731.428571 + -1731.428571 = 0.000000 0.000000 + -85x + x2 = 0 + -1731.428571 -85x + x2 = 0 + -1731.428571 Combine like terms: 0 + -1731.428571 = -1731.428571 -85x + x2 = -1731.428571 The x term is -85x. Take half its coefficient (-42.5). Square it (1806.25) and add it to both sides. Add '1806.25' to each side of the equation. -85x + 1806.25 + x2 = -1731.428571 + 1806.25 Reorder the terms: 1806.25 + -85x + x2 = -1731.428571 + 1806.25 Combine like terms: -1731.428571 + 1806.25 = 74.821429 1806.25 + -85x + x2 = 74.821429 Factor a perfect square on the left side: (x + -42.5)(x + -42.5) = 74.821429 Calculate the square root of the right side: 8.649938092 Break this problem into two subproblems by setting (x + -42.5) equal to 8.649938092 and -8.649938092.Subproblem 1
x + -42.5 = 8.649938092 Simplifying x + -42.5 = 8.649938092 Reorder the terms: -42.5 + x = 8.649938092 Solving -42.5 + x = 8.649938092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = 8.649938092 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = 8.649938092 + 42.5 x = 8.649938092 + 42.5 Combine like terms: 8.649938092 + 42.5 = 51.149938092 x = 51.149938092 Simplifying x = 51.149938092Subproblem 2
x + -42.5 = -8.649938092 Simplifying x + -42.5 = -8.649938092 Reorder the terms: -42.5 + x = -8.649938092 Solving -42.5 + x = -8.649938092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = -8.649938092 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = -8.649938092 + 42.5 x = -8.649938092 + 42.5 Combine like terms: -8.649938092 + 42.5 = 33.850061908 x = 33.850061908 Simplifying x = 33.850061908Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.149938092, 33.850061908}
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