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Simplifying 358 = -0.5x2 + 36x + -236 Reorder the terms: 358 = -236 + 36x + -0.5x2 Solving 358 = -236 + 36x + -0.5x2 Solving for variable 'x'. Combine like terms: 358 + 236 = 594 594 + -36x + 0.5x2 = -236 + 36x + -0.5x2 + 236 + -36x + 0.5x2 Reorder the terms: 594 + -36x + 0.5x2 = -236 + 236 + 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: -236 + 236 = 0 594 + -36x + 0.5x2 = 0 + 36x + -36x + -0.5x2 + 0.5x2 594 + -36x + 0.5x2 = 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: 36x + -36x = 0 594 + -36x + 0.5x2 = 0 + -0.5x2 + 0.5x2 594 + -36x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 594 + -36x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 1188 + -72x + x2 = 0 Move the constant term to the right: Add '-1188' to each side of the equation. 1188 + -72x + -1188 + x2 = 0 + -1188 Reorder the terms: 1188 + -1188 + -72x + x2 = 0 + -1188 Combine like terms: 1188 + -1188 = 0 0 + -72x + x2 = 0 + -1188 -72x + x2 = 0 + -1188 Combine like terms: 0 + -1188 = -1188 -72x + x2 = -1188 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = -1188 + 1296 Reorder the terms: 1296 + -72x + x2 = -1188 + 1296 Combine like terms: -1188 + 1296 = 108 1296 + -72x + x2 = 108 Factor a perfect square on the left side: (x + -36)(x + -36) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + -36) equal to 10.392304845 and -10.392304845.Subproblem 1
x + -36 = 10.392304845 Simplifying x + -36 = 10.392304845 Reorder the terms: -36 + x = 10.392304845 Solving -36 + x = 10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 10.392304845 + 36 Combine like terms: -36 + 36 = 0 0 + x = 10.392304845 + 36 x = 10.392304845 + 36 Combine like terms: 10.392304845 + 36 = 46.392304845 x = 46.392304845 Simplifying x = 46.392304845Subproblem 2
x + -36 = -10.392304845 Simplifying x + -36 = -10.392304845 Reorder the terms: -36 + x = -10.392304845 Solving -36 + x = -10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -10.392304845 + 36 Combine like terms: -36 + 36 = 0 0 + x = -10.392304845 + 36 x = -10.392304845 + 36 Combine like terms: -10.392304845 + 36 = 25.607695155 x = 25.607695155 Simplifying x = 25.607695155Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.392304845, 25.607695155}
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