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Simplifying 0 = -0.5x2 + 25x + -150 Reorder the terms: 0 = -150 + 25x + -0.5x2 Solving 0 = -150 + 25x + -0.5x2 Solving for variable 'x'. Combine like terms: 0 + 150 = 150 150 + -25x + 0.5x2 = -150 + 25x + -0.5x2 + 150 + -25x + 0.5x2 Reorder the terms: 150 + -25x + 0.5x2 = -150 + 150 + 25x + -25x + -0.5x2 + 0.5x2 Combine like terms: -150 + 150 = 0 150 + -25x + 0.5x2 = 0 + 25x + -25x + -0.5x2 + 0.5x2 150 + -25x + 0.5x2 = 25x + -25x + -0.5x2 + 0.5x2 Combine like terms: 25x + -25x = 0 150 + -25x + 0.5x2 = 0 + -0.5x2 + 0.5x2 150 + -25x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 150 + -25x + 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'. 300 + -50x + x2 = 0 Move the constant term to the right: Add '-300' to each side of the equation. 300 + -50x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -50x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -50x + x2 = 0 + -300 -50x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -50x + x2 = -300 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -300 + 625 Reorder the terms: 625 + -50x + x2 = -300 + 625 Combine like terms: -300 + 625 = 325 625 + -50x + x2 = 325 Factor a perfect square on the left side: (x + -25)(x + -25) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (x + -25) equal to 18.027756377 and -18.027756377.Subproblem 1
x + -25 = 18.027756377 Simplifying x + -25 = 18.027756377 Reorder the terms: -25 + x = 18.027756377 Solving -25 + x = 18.027756377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 18.027756377 + 25 Combine like terms: -25 + 25 = 0 0 + x = 18.027756377 + 25 x = 18.027756377 + 25 Combine like terms: 18.027756377 + 25 = 43.027756377 x = 43.027756377 Simplifying x = 43.027756377Subproblem 2
x + -25 = -18.027756377 Simplifying x + -25 = -18.027756377 Reorder the terms: -25 + x = -18.027756377 Solving -25 + x = -18.027756377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -18.027756377 + 25 Combine like terms: -25 + 25 = 0 0 + x = -18.027756377 + 25 x = -18.027756377 + 25 Combine like terms: -18.027756377 + 25 = 6.972243623 x = 6.972243623 Simplifying x = 6.972243623Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.027756377, 6.972243623}
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