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Simplifying 0 = -0.5x2 + 36x + -522 Reorder the terms: 0 = -522 + 36x + -0.5x2 Solving 0 = -522 + 36x + -0.5x2 Solving for variable 'x'. Combine like terms: 0 + 522 = 522 522 + -36x + 0.5x2 = -522 + 36x + -0.5x2 + 522 + -36x + 0.5x2 Reorder the terms: 522 + -36x + 0.5x2 = -522 + 522 + 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: -522 + 522 = 0 522 + -36x + 0.5x2 = 0 + 36x + -36x + -0.5x2 + 0.5x2 522 + -36x + 0.5x2 = 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: 36x + -36x = 0 522 + -36x + 0.5x2 = 0 + -0.5x2 + 0.5x2 522 + -36x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 522 + -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'. 1044 + -72x + x2 = 0 Move the constant term to the right: Add '-1044' to each side of the equation. 1044 + -72x + -1044 + x2 = 0 + -1044 Reorder the terms: 1044 + -1044 + -72x + x2 = 0 + -1044 Combine like terms: 1044 + -1044 = 0 0 + -72x + x2 = 0 + -1044 -72x + x2 = 0 + -1044 Combine like terms: 0 + -1044 = -1044 -72x + x2 = -1044 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 = -1044 + 1296 Reorder the terms: 1296 + -72x + x2 = -1044 + 1296 Combine like terms: -1044 + 1296 = 252 1296 + -72x + x2 = 252 Factor a perfect square on the left side: (x + -36)(x + -36) = 252 Calculate the square root of the right side: 15.874507866 Break this problem into two subproblems by setting (x + -36) equal to 15.874507866 and -15.874507866.Subproblem 1
x + -36 = 15.874507866 Simplifying x + -36 = 15.874507866 Reorder the terms: -36 + x = 15.874507866 Solving -36 + x = 15.874507866 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 = 15.874507866 + 36 Combine like terms: -36 + 36 = 0 0 + x = 15.874507866 + 36 x = 15.874507866 + 36 Combine like terms: 15.874507866 + 36 = 51.874507866 x = 51.874507866 Simplifying x = 51.874507866Subproblem 2
x + -36 = -15.874507866 Simplifying x + -36 = -15.874507866 Reorder the terms: -36 + x = -15.874507866 Solving -36 + x = -15.874507866 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 = -15.874507866 + 36 Combine like terms: -36 + 36 = 0 0 + x = -15.874507866 + 36 x = -15.874507866 + 36 Combine like terms: -15.874507866 + 36 = 20.125492134 x = 20.125492134 Simplifying x = 20.125492134Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.874507866, 20.125492134}
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