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Simplifying 60 = -1.5x2 + 18x + 6 Reorder the terms: 60 = 6 + 18x + -1.5x2 Solving 60 = 6 + 18x + -1.5x2 Solving for variable 'x'. Combine like terms: 60 + -6 = 54 54 + -18x + 1.5x2 = 6 + 18x + -1.5x2 + -6 + -18x + 1.5x2 Reorder the terms: 54 + -18x + 1.5x2 = 6 + -6 + 18x + -18x + -1.5x2 + 1.5x2 Combine like terms: 6 + -6 = 0 54 + -18x + 1.5x2 = 0 + 18x + -18x + -1.5x2 + 1.5x2 54 + -18x + 1.5x2 = 18x + -18x + -1.5x2 + 1.5x2 Combine like terms: 18x + -18x = 0 54 + -18x + 1.5x2 = 0 + -1.5x2 + 1.5x2 54 + -18x + 1.5x2 = -1.5x2 + 1.5x2 Combine like terms: -1.5x2 + 1.5x2 = 0.0 54 + -18x + 1.5x2 = 0.0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 36 + -12x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -12x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -12x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -12x + x2 = 0 + -36 -12x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -12x + x2 = -36 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -36 + 36 Reorder the terms: 36 + -12x + x2 = -36 + 36 Combine like terms: -36 + 36 = 0 36 + -12x + x2 = 0 Factor a perfect square on the left side: (x + -6)(x + -6) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -6) equal to 0 and 0.Subproblem 1
x + -6 = 0 Simplifying x + -6 = 0 Reorder the terms: -6 + x = 0 Solving -6 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 2
x + -6 = 0 Simplifying x + -6 = 0 Reorder the terms: -6 + x = 0 Solving -6 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, 6}
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