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Simplifying 252 = (0.5)(x)(x + -3) Reorder the terms: 252 = 0.5x(-3 + x) 252 = (-3 * 0.5x + x * 0.5x) 252 = (-1.5x + 0.5x2) Solving 252 = -1.5x + 0.5x2 Solving for variable 'x'. Reorder the terms: 252 + 1.5x + -0.5x2 = -1.5x + 1.5x + 0.5x2 + -0.5x2 Combine like terms: -1.5x + 1.5x = 0.0 252 + 1.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2 252 + 1.5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 252 + 1.5x + -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'. -504 + -3x + x2 = 0 Move the constant term to the right: Add '504' to each side of the equation. -504 + -3x + 504 + x2 = 0 + 504 Reorder the terms: -504 + 504 + -3x + x2 = 0 + 504 Combine like terms: -504 + 504 = 0 0 + -3x + x2 = 0 + 504 -3x + x2 = 0 + 504 Combine like terms: 0 + 504 = 504 -3x + x2 = 504 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 504 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 504 + 2.25 Combine like terms: 504 + 2.25 = 506.25 2.25 + -3x + x2 = 506.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 506.25 Calculate the square root of the right side: 22.5 Break this problem into two subproblems by setting (x + -1.5) equal to 22.5 and -22.5.Subproblem 1
x + -1.5 = 22.5 Simplifying x + -1.5 = 22.5 Reorder the terms: -1.5 + x = 22.5 Solving -1.5 + x = 22.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 22.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 22.5 + 1.5 x = 22.5 + 1.5 Combine like terms: 22.5 + 1.5 = 24 x = 24 Simplifying x = 24Subproblem 2
x + -1.5 = -22.5 Simplifying x + -1.5 = -22.5 Reorder the terms: -1.5 + x = -22.5 Solving -1.5 + x = -22.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -22.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -22.5 + 1.5 x = -22.5 + 1.5 Combine like terms: -22.5 + 1.5 = -21 x = -21 Simplifying x = -21Solution
The solution to the problem is based on the solutions from the subproblems. x = {24, -21}
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