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Simplifying x(x + -33) = 150 Reorder the terms: x(-33 + x) = 150 (-33 * x + x * x) = 150 (-33x + x2) = 150 Solving -33x + x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + -33x + x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + -33x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + -33x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + -33x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -33x + x2 = 0 + 150 -33x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 -33x + x2 = 150 The x term is -33x. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33x + 272.25 + x2 = 150 + 272.25 Reorder the terms: 272.25 + -33x + x2 = 150 + 272.25 Combine like terms: 150 + 272.25 = 422.25 272.25 + -33x + x2 = 422.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 422.25 Calculate the square root of the right side: 20.548722588 Break this problem into two subproblems by setting (x + -16.5) equal to 20.548722588 and -20.548722588.Subproblem 1
x + -16.5 = 20.548722588 Simplifying x + -16.5 = 20.548722588 Reorder the terms: -16.5 + x = 20.548722588 Solving -16.5 + x = 20.548722588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = 20.548722588 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 20.548722588 + 16.5 x = 20.548722588 + 16.5 Combine like terms: 20.548722588 + 16.5 = 37.048722588 x = 37.048722588 Simplifying x = 37.048722588Subproblem 2
x + -16.5 = -20.548722588 Simplifying x + -16.5 = -20.548722588 Reorder the terms: -16.5 + x = -20.548722588 Solving -16.5 + x = -20.548722588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = -20.548722588 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -20.548722588 + 16.5 x = -20.548722588 + 16.5 Combine like terms: -20.548722588 + 16.5 = -4.048722588 x = -4.048722588 Simplifying x = -4.048722588Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.048722588, -4.048722588}
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