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Simplifying 400 = 0.0119x2 + -45.585x + 43728 Reorder the terms: 400 = 43728 + -45.585x + 0.0119x2 Solving 400 = 43728 + -45.585x + 0.0119x2 Solving for variable 'x'. Combine like terms: 400 + -43728 = -43328 -43328 + 45.585x + -0.0119x2 = 43728 + -45.585x + 0.0119x2 + -43728 + 45.585x + -0.0119x2 Reorder the terms: -43328 + 45.585x + -0.0119x2 = 43728 + -43728 + -45.585x + 45.585x + 0.0119x2 + -0.0119x2 Combine like terms: 43728 + -43728 = 0 -43328 + 45.585x + -0.0119x2 = 0 + -45.585x + 45.585x + 0.0119x2 + -0.0119x2 -43328 + 45.585x + -0.0119x2 = -45.585x + 45.585x + 0.0119x2 + -0.0119x2 Combine like terms: -45.585x + 45.585x = 0.000 -43328 + 45.585x + -0.0119x2 = 0.000 + 0.0119x2 + -0.0119x2 -43328 + 45.585x + -0.0119x2 = 0.0119x2 + -0.0119x2 Combine like terms: 0.0119x2 + -0.0119x2 = 0.0000 -43328 + 45.585x + -0.0119x2 = 0.0000 Begin completing the square. Divide all terms by -0.0119 the coefficient of the squared term: Divide each side by '-0.0119'. 3641008.403 + -3830.672269x + x2 = 0 Move the constant term to the right: Add '-3641008.403' to each side of the equation. 3641008.403 + -3830.672269x + -3641008.403 + x2 = 0 + -3641008.403 Reorder the terms: 3641008.403 + -3641008.403 + -3830.672269x + x2 = 0 + -3641008.403 Combine like terms: 3641008.403 + -3641008.403 = 0.000 0.000 + -3830.672269x + x2 = 0 + -3641008.403 -3830.672269x + x2 = 0 + -3641008.403 Combine like terms: 0 + -3641008.403 = -3641008.403 -3830.672269x + x2 = -3641008.403 The x term is -3830.672269x. Take half its coefficient (-1915.336135). Square it (3668512.510) and add it to both sides. Add '3668512.510' to each side of the equation. -3830.672269x + 3668512.510 + x2 = -3641008.403 + 3668512.510 Reorder the terms: 3668512.510 + -3830.672269x + x2 = -3641008.403 + 3668512.510 Combine like terms: -3641008.403 + 3668512.510 = 27504.107 3668512.510 + -3830.672269x + x2 = 27504.107 Factor a perfect square on the left side: (x + -1915.336135)(x + -1915.336135) = 27504.107 Calculate the square root of the right side: 165.843622126 Break this problem into two subproblems by setting (x + -1915.336135) equal to 165.843622126 and -165.843622126.Subproblem 1
x + -1915.336135 = 165.843622126 Simplifying x + -1915.336135 = 165.843622126 Reorder the terms: -1915.336135 + x = 165.843622126 Solving -1915.336135 + x = 165.843622126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1915.336135' to each side of the equation. -1915.336135 + 1915.336135 + x = 165.843622126 + 1915.336135 Combine like terms: -1915.336135 + 1915.336135 = 0.000000 0.000000 + x = 165.843622126 + 1915.336135 x = 165.843622126 + 1915.336135 Combine like terms: 165.843622126 + 1915.336135 = 2081.179757126 x = 2081.179757126 Simplifying x = 2081.179757126Subproblem 2
x + -1915.336135 = -165.843622126 Simplifying x + -1915.336135 = -165.843622126 Reorder the terms: -1915.336135 + x = -165.843622126 Solving -1915.336135 + x = -165.843622126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1915.336135' to each side of the equation. -1915.336135 + 1915.336135 + x = -165.843622126 + 1915.336135 Combine like terms: -1915.336135 + 1915.336135 = 0.000000 0.000000 + x = -165.843622126 + 1915.336135 x = -165.843622126 + 1915.336135 Combine like terms: -165.843622126 + 1915.336135 = 1749.492512874 x = 1749.492512874 Simplifying x = 1749.492512874Solution
The solution to the problem is based on the solutions from the subproblems. x = {2081.179757126, 1749.492512874}
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