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Simplifying -1.5x2 + 33x + -75 = 0 Reorder the terms: -75 + 33x + -1.5x2 = 0 Solving -75 + 33x + -1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. 50 + -22x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -22x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -22x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -22x + x2 = 0 + -50 -22x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -22x + x2 = -50 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 = -50 + 121 Reorder the terms: 121 + -22x + x2 = -50 + 121 Combine like terms: -50 + 121 = 71 121 + -22x + x2 = 71 Factor a perfect square on the left side: (x + -11)(x + -11) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + -11) equal to 8.426149773 and -8.426149773.Subproblem 1
x + -11 = 8.426149773 Simplifying x + -11 = 8.426149773 Reorder the terms: -11 + x = 8.426149773 Solving -11 + x = 8.426149773 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 = 8.426149773 + 11 Combine like terms: -11 + 11 = 0 0 + x = 8.426149773 + 11 x = 8.426149773 + 11 Combine like terms: 8.426149773 + 11 = 19.426149773 x = 19.426149773 Simplifying x = 19.426149773Subproblem 2
x + -11 = -8.426149773 Simplifying x + -11 = -8.426149773 Reorder the terms: -11 + x = -8.426149773 Solving -11 + x = -8.426149773 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 = -8.426149773 + 11 Combine like terms: -11 + 11 = 0 0 + x = -8.426149773 + 11 x = -8.426149773 + 11 Combine like terms: -8.426149773 + 11 = 2.573850227 x = 2.573850227 Simplifying x = 2.573850227Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.426149773, 2.573850227}
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