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Simplifying 3x2 + 17x + -12 = 0 Reorder the terms: -12 + 17x + 3x2 = 0 Solving -12 + 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'. -4 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 5.666666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 5.666666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5.666666667x + x2 = 0 + 4 5.666666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 5.666666667x + x2 = 4 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 = 4 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 4 + 8.027777782 Combine like terms: 4 + 8.027777782 = 12.027777782 8.027777782 + 5.666666667x + x2 = 12.027777782 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 12.027777782 Calculate the square root of the right side: 3.468108675 Break this problem into two subproblems by setting (x + 2.833333334) equal to 3.468108675 and -3.468108675.Subproblem 1
x + 2.833333334 = 3.468108675 Simplifying x + 2.833333334 = 3.468108675 Reorder the terms: 2.833333334 + x = 3.468108675 Solving 2.833333334 + x = 3.468108675 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 = 3.468108675 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 3.468108675 + -2.833333334 x = 3.468108675 + -2.833333334 Combine like terms: 3.468108675 + -2.833333334 = 0.634775341 x = 0.634775341 Simplifying x = 0.634775341Subproblem 2
x + 2.833333334 = -3.468108675 Simplifying x + 2.833333334 = -3.468108675 Reorder the terms: 2.833333334 + x = -3.468108675 Solving 2.833333334 + x = -3.468108675 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 = -3.468108675 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -3.468108675 + -2.833333334 x = -3.468108675 + -2.833333334 Combine like terms: -3.468108675 + -2.833333334 = -6.301442009 x = -6.301442009 Simplifying x = -6.301442009Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.634775341, -6.301442009}
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