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Simplifying 3x2 + 17x + -76 = 0 Reorder the terms: -76 + 17x + 3x2 = 0 Solving -76 + 17x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -25.33333333 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '25.33333333' to each side of the equation. -25.33333333 + 5.666666667x + 25.33333333 + x2 = 0 + 25.33333333 Reorder the terms: -25.33333333 + 25.33333333 + 5.666666667x + x2 = 0 + 25.33333333 Combine like terms: -25.33333333 + 25.33333333 = 0.00000000 0.00000000 + 5.666666667x + x2 = 0 + 25.33333333 5.666666667x + x2 = 0 + 25.33333333 Combine like terms: 0 + 25.33333333 = 25.33333333 5.666666667x + x2 = 25.33333333 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 = 25.33333333 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 25.33333333 + 8.027777782 Combine like terms: 25.33333333 + 8.027777782 = 33.361111112 8.027777782 + 5.666666667x + x2 = 33.361111112 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 33.361111112 Calculate the square root of the right side: 5.775907817 Break this problem into two subproblems by setting (x + 2.833333334) equal to 5.775907817 and -5.775907817.Subproblem 1
x + 2.833333334 = 5.775907817 Simplifying x + 2.833333334 = 5.775907817 Reorder the terms: 2.833333334 + x = 5.775907817 Solving 2.833333334 + x = 5.775907817 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 = 5.775907817 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 5.775907817 + -2.833333334 x = 5.775907817 + -2.833333334 Combine like terms: 5.775907817 + -2.833333334 = 2.942574483 x = 2.942574483 Simplifying x = 2.942574483Subproblem 2
x + 2.833333334 = -5.775907817 Simplifying x + 2.833333334 = -5.775907817 Reorder the terms: 2.833333334 + x = -5.775907817 Solving 2.833333334 + x = -5.775907817 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 = -5.775907817 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -5.775907817 + -2.833333334 x = -5.775907817 + -2.833333334 Combine like terms: -5.775907817 + -2.833333334 = -8.609241151 x = -8.609241151 Simplifying x = -8.609241151Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.942574483, -8.609241151}
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