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Simplifying -1.5x2 + 33x + -75 = 52.5 Reorder the terms: -75 + 33x + -1.5x2 = 52.5 Solving -75 + 33x + -1.5x2 = 52.5 Solving for variable 'x'. Reorder the terms: -75 + -52.5 + 33x + -1.5x2 = 52.5 + -52.5 Combine like terms: -75 + -52.5 = -127.5 -127.5 + 33x + -1.5x2 = 52.5 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 -127.5 + 33x + -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'. 85 + -22x + x2 = 0 Move the constant term to the right: Add '-85' to each side of the equation. 85 + -22x + -85 + x2 = 0 + -85 Reorder the terms: 85 + -85 + -22x + x2 = 0 + -85 Combine like terms: 85 + -85 = 0 0 + -22x + x2 = 0 + -85 -22x + x2 = 0 + -85 Combine like terms: 0 + -85 = -85 -22x + x2 = -85 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -85 + 121 Reorder the terms: 121 + -22x + x2 = -85 + 121 Combine like terms: -85 + 121 = 36 121 + -22x + x2 = 36 Factor a perfect square on the left side: (x + -11)(x + -11) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + -11) equal to 6 and -6.Subproblem 1
x + -11 = 6 Simplifying x + -11 = 6 Reorder the terms: -11 + x = 6 Solving -11 + x = 6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 6 + 11 Combine like terms: -11 + 11 = 0 0 + x = 6 + 11 x = 6 + 11 Combine like terms: 6 + 11 = 17 x = 17 Simplifying x = 17Subproblem 2
x + -11 = -6 Simplifying x + -11 = -6 Reorder the terms: -11 + x = -6 Solving -11 + x = -6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -6 + 11 Combine like terms: -11 + 11 = 0 0 + x = -6 + 11 x = -6 + 11 Combine like terms: -6 + 11 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {17, 5}
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