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Simplifying 0 = 3x2 + -17x + 12 Reorder the terms: 0 = 12 + -17x + 3x2 Solving 0 = 12 + -17x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + 17x + -3x2 = 12 + -17x + 3x2 + -12 + 17x + -3x2 Reorder the terms: -12 + 17x + -3x2 = 12 + -12 + -17x + 17x + 3x2 + -3x2 Combine like terms: 12 + -12 = 0 -12 + 17x + -3x2 = 0 + -17x + 17x + 3x2 + -3x2 -12 + 17x + -3x2 = -17x + 17x + 3x2 + -3x2 Combine like terms: -17x + 17x = 0 -12 + 17x + -3x2 = 0 + 3x2 + -3x2 -12 + 17x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -12 + 17x + -3x2 = 0 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 = 4.027777782 8.027777782 + -5.666666667x + x2 = 4.027777782 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 4.027777782 Calculate the square root of the right side: 2.006932431 Break this problem into two subproblems by setting (x + -2.833333334) equal to 2.006932431 and -2.006932431.Subproblem 1
x + -2.833333334 = 2.006932431 Simplifying x + -2.833333334 = 2.006932431 Reorder the terms: -2.833333334 + x = 2.006932431 Solving -2.833333334 + x = 2.006932431 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 = 2.006932431 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 2.006932431 + 2.833333334 x = 2.006932431 + 2.833333334 Combine like terms: 2.006932431 + 2.833333334 = 4.840265765 x = 4.840265765 Simplifying x = 4.840265765Subproblem 2
x + -2.833333334 = -2.006932431 Simplifying x + -2.833333334 = -2.006932431 Reorder the terms: -2.833333334 + x = -2.006932431 Solving -2.833333334 + x = -2.006932431 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 = -2.006932431 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -2.006932431 + 2.833333334 x = -2.006932431 + 2.833333334 Combine like terms: -2.006932431 + 2.833333334 = 0.826400903 x = 0.826400903 Simplifying x = 0.826400903Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.840265765, 0.826400903}
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