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Simplifying 0.5(x + -6) * x = 13.5 Reorder the terms: 0.5(-6 + x) * x = 13.5 Reorder the terms for easier multiplication: 0.5x(-6 + x) = 13.5 (-6 * 0.5x + x * 0.5x) = 13.5 (-3x + 0.5x2) = 13.5 Solving -3x + 0.5x2 = 13.5 Solving for variable 'x'. Reorder the terms: -13.5 + -3x + 0.5x2 = 13.5 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 -13.5 + -3x + 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'. -27 + -6x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -6x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -6x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -6x + x2 = 0 + 27 -6x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -6x + x2 = 27 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 27 + 9 Reorder the terms: 9 + -6x + x2 = 27 + 9 Combine like terms: 27 + 9 = 36 9 + -6x + x2 = 36 Factor a perfect square on the left side: (x + -3)(x + -3) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + -3) equal to 6 and -6.Subproblem 1
x + -3 = 6 Simplifying x + -3 = 6 Reorder the terms: -3 + x = 6 Solving -3 + x = 6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 6 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6 + 3 x = 6 + 3 Combine like terms: 6 + 3 = 9 x = 9 Simplifying x = 9Subproblem 2
x + -3 = -6 Simplifying x + -3 = -6 Reorder the terms: -3 + x = -6 Solving -3 + x = -6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -6 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6 + 3 x = -6 + 3 Combine like terms: -6 + 3 = -3 x = -3 Simplifying x = -3Solution
The solution to the problem is based on the solutions from the subproblems. x = {9, -3}
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