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Simplifying -1.5x2 + 33x + -75 = 106.50 Reorder the terms: -75 + 33x + -1.5x2 = 106.50 Solving -75 + 33x + -1.5x2 = 106.50 Solving for variable 'x'. Reorder the terms: -75 + -106.50 + 33x + -1.5x2 = 106.50 + -106.50 Combine like terms: -75 + -106.50 = -181.5 -181.5 + 33x + -1.5x2 = 106.50 + -106.50 Combine like terms: 106.50 + -106.50 = 0.00 -181.5 + 33x + -1.5x2 = 0.00 Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. 121 + -22x + x2 = 0.0 Move the constant term to the right: Add '-121' to each side of the equation. 121 + -22x + -121 + x2 = 0.0 + -121 Reorder the terms: 121 + -121 + -22x + x2 = 0.0 + -121 Combine like terms: 121 + -121 = 0 0 + -22x + x2 = 0.0 + -121 -22x + x2 = 0.0 + -121 Combine like terms: 0.0 + -121 = -121 -22x + x2 = -121 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 = -121 + 121 Reorder the terms: 121 + -22x + x2 = -121 + 121 Combine like terms: -121 + 121 = 0 121 + -22x + x2 = 0 Factor a perfect square on the left side: (x + -11)(x + -11) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -11) equal to 0 and 0.Subproblem 1
x + -11 = 0 Simplifying x + -11 = 0 Reorder the terms: -11 + x = 0 Solving -11 + x = 0 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 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Simplifying x = 11Subproblem 2
x + -11 = 0 Simplifying x + -11 = 0 Reorder the terms: -11 + x = 0 Solving -11 + x = 0 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 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Simplifying x = 11Solution
The solution to the problem is based on the solutions from the subproblems. x = {11, 11}
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