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Simplifying 0 = 3x2 + -17x + -66 Reorder the terms: 0 = -66 + -17x + 3x2 Solving 0 = -66 + -17x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 66 = 66 66 + 17x + -3x2 = -66 + -17x + 3x2 + 66 + 17x + -3x2 Reorder the terms: 66 + 17x + -3x2 = -66 + 66 + -17x + 17x + 3x2 + -3x2 Combine like terms: -66 + 66 = 0 66 + 17x + -3x2 = 0 + -17x + 17x + 3x2 + -3x2 66 + 17x + -3x2 = -17x + 17x + 3x2 + -3x2 Combine like terms: -17x + 17x = 0 66 + 17x + -3x2 = 0 + 3x2 + -3x2 66 + 17x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 66 + 17x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -22 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + -5.666666667x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -5.666666667x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -5.666666667x + x2 = 0 + 22 -5.666666667x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -5.666666667x + x2 = 22 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = 22 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 22 + 8.027777782 Combine like terms: 22 + 8.027777782 = 30.027777782 8.027777782 + -5.666666667x + x2 = 30.027777782 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 30.027777782 Calculate the square root of the right side: 5.479760741 Break this problem into two subproblems by setting (x + -2.833333334) equal to 5.479760741 and -5.479760741.Subproblem 1
x + -2.833333334 = 5.479760741 Simplifying x + -2.833333334 = 5.479760741 Reorder the terms: -2.833333334 + x = 5.479760741 Solving -2.833333334 + x = 5.479760741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 5.479760741 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 5.479760741 + 2.833333334 x = 5.479760741 + 2.833333334 Combine like terms: 5.479760741 + 2.833333334 = 8.313094075 x = 8.313094075 Simplifying x = 8.313094075Subproblem 2
x + -2.833333334 = -5.479760741 Simplifying x + -2.833333334 = -5.479760741 Reorder the terms: -2.833333334 + x = -5.479760741 Solving -2.833333334 + x = -5.479760741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -5.479760741 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -5.479760741 + 2.833333334 x = -5.479760741 + 2.833333334 Combine like terms: -5.479760741 + 2.833333334 = -2.646427407 x = -2.646427407 Simplifying x = -2.646427407Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.313094075, -2.646427407}
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