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Simplifying 0 = 3x2 + 17x + -5 Reorder the terms: 0 = -5 + 17x + 3x2 Solving 0 = -5 + 17x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + -17x + -3x2 = -5 + 17x + 3x2 + 5 + -17x + -3x2 Reorder the terms: 5 + -17x + -3x2 = -5 + 5 + 17x + -17x + 3x2 + -3x2 Combine like terms: -5 + 5 = 0 5 + -17x + -3x2 = 0 + 17x + -17x + 3x2 + -3x2 5 + -17x + -3x2 = 17x + -17x + 3x2 + -3x2 Combine like terms: 17x + -17x = 0 5 + -17x + -3x2 = 0 + 3x2 + -3x2 5 + -17x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 5 + -17x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.666666667 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 5.666666667x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 5.666666667x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 5.666666667x + x2 = 0 + 1.666666667 5.666666667x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 5.666666667x + x2 = 1.666666667 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 = 1.666666667 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 1.666666667 + 8.027777782 Combine like terms: 1.666666667 + 8.027777782 = 9.694444449 8.027777782 + 5.666666667x + x2 = 9.694444449 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 9.694444449 Calculate the square root of the right side: 3.113590283 Break this problem into two subproblems by setting (x + 2.833333334) equal to 3.113590283 and -3.113590283.Subproblem 1
x + 2.833333334 = 3.113590283 Simplifying x + 2.833333334 = 3.113590283 Reorder the terms: 2.833333334 + x = 3.113590283 Solving 2.833333334 + x = 3.113590283 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 = 3.113590283 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 3.113590283 + -2.833333334 x = 3.113590283 + -2.833333334 Combine like terms: 3.113590283 + -2.833333334 = 0.280256949 x = 0.280256949 Simplifying x = 0.280256949Subproblem 2
x + 2.833333334 = -3.113590283 Simplifying x + 2.833333334 = -3.113590283 Reorder the terms: 2.833333334 + x = -3.113590283 Solving 2.833333334 + x = -3.113590283 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 = -3.113590283 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -3.113590283 + -2.833333334 x = -3.113590283 + -2.833333334 Combine like terms: -3.113590283 + -2.833333334 = -5.946923617 x = -5.946923617 Simplifying x = -5.946923617Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.280256949, -5.946923617}
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