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Simplifying 0 = 17x + -7 + 3x2 Reorder the terms: 0 = -7 + 17x + 3x2 Solving 0 = -7 + 17x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + -17x + -3x2 = -7 + 17x + 3x2 + 7 + -17x + -3x2 Reorder the terms: 7 + -17x + -3x2 = -7 + 7 + 17x + -17x + 3x2 + -3x2 Combine like terms: -7 + 7 = 0 7 + -17x + -3x2 = 0 + 17x + -17x + 3x2 + -3x2 7 + -17x + -3x2 = 17x + -17x + 3x2 + -3x2 Combine like terms: 17x + -17x = 0 7 + -17x + -3x2 = 0 + 3x2 + -3x2 7 + -17x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 7 + -17x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.333333333 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 5.666666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 5.666666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 5.666666667x + x2 = 0 + 2.333333333 5.666666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 5.666666667x + x2 = 2.333333333 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 = 2.333333333 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 2.333333333 + 8.027777782 Combine like terms: 2.333333333 + 8.027777782 = 10.361111115 8.027777782 + 5.666666667x + x2 = 10.361111115 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 10.361111115 Calculate the square root of the right side: 3.218867987 Break this problem into two subproblems by setting (x + 2.833333334) equal to 3.218867987 and -3.218867987.Subproblem 1
x + 2.833333334 = 3.218867987 Simplifying x + 2.833333334 = 3.218867987 Reorder the terms: 2.833333334 + x = 3.218867987 Solving 2.833333334 + x = 3.218867987 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 = 3.218867987 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 3.218867987 + -2.833333334 x = 3.218867987 + -2.833333334 Combine like terms: 3.218867987 + -2.833333334 = 0.385534653 x = 0.385534653 Simplifying x = 0.385534653Subproblem 2
x + 2.833333334 = -3.218867987 Simplifying x + 2.833333334 = -3.218867987 Reorder the terms: 2.833333334 + x = -3.218867987 Solving 2.833333334 + x = -3.218867987 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 = -3.218867987 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -3.218867987 + -2.833333334 x = -3.218867987 + -2.833333334 Combine like terms: -3.218867987 + -2.833333334 = -6.052201321 x = -6.052201321 Simplifying x = -6.052201321Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.385534653, -6.052201321}
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