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Simplifying -0.5x2 + 36x + -612 = 0 Reorder the terms: -612 + 36x + -0.5x2 = 0 Solving -612 + 36x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 1224 + -72x + x2 = 0 Move the constant term to the right: Add '-1224' to each side of the equation. 1224 + -72x + -1224 + x2 = 0 + -1224 Reorder the terms: 1224 + -1224 + -72x + x2 = 0 + -1224 Combine like terms: 1224 + -1224 = 0 0 + -72x + x2 = 0 + -1224 -72x + x2 = 0 + -1224 Combine like terms: 0 + -1224 = -1224 -72x + x2 = -1224 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 = -1224 + 1296 Reorder the terms: 1296 + -72x + x2 = -1224 + 1296 Combine like terms: -1224 + 1296 = 72 1296 + -72x + x2 = 72 Factor a perfect square on the left side: (x + -36)(x + -36) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + -36) equal to 8.485281374 and -8.485281374.Subproblem 1
x + -36 = 8.485281374 Simplifying x + -36 = 8.485281374 Reorder the terms: -36 + x = 8.485281374 Solving -36 + x = 8.485281374 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 = 8.485281374 + 36 Combine like terms: -36 + 36 = 0 0 + x = 8.485281374 + 36 x = 8.485281374 + 36 Combine like terms: 8.485281374 + 36 = 44.485281374 x = 44.485281374 Simplifying x = 44.485281374Subproblem 2
x + -36 = -8.485281374 Simplifying x + -36 = -8.485281374 Reorder the terms: -36 + x = -8.485281374 Solving -36 + x = -8.485281374 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 = -8.485281374 + 36 Combine like terms: -36 + 36 = 0 0 + x = -8.485281374 + 36 x = -8.485281374 + 36 Combine like terms: -8.485281374 + 36 = 27.514718626 x = 27.514718626 Simplifying x = 27.514718626Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.485281374, 27.514718626}
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