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Simplifying 6x2 + -34x = 16 Reorder the terms: -34x + 6x2 = 16 Solving -34x + 6x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + -34x + 6x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -34x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -17x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -17x + 3x2)' equal to zero and attempt to solve: Simplifying -8 + -17x + 3x2 = 0 Solving -8 + -17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -5.666666667x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -5.666666667x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -5.666666667x + x2 = 0 + 2.666666667 -5.666666667x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -5.666666667x + x2 = 2.666666667 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 = 2.666666667 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 2.666666667 + 8.027777782 Combine like terms: 2.666666667 + 8.027777782 = 10.694444449 8.027777782 + -5.666666667x + x2 = 10.694444449 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 10.694444449 Calculate the square root of the right side: 3.270236146 Break this problem into two subproblems by setting (x + -2.833333334) equal to 3.270236146 and -3.270236146.Subproblem 1
x + -2.833333334 = 3.270236146 Simplifying x + -2.833333334 = 3.270236146 Reorder the terms: -2.833333334 + x = 3.270236146 Solving -2.833333334 + x = 3.270236146 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 = 3.270236146 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 3.270236146 + 2.833333334 x = 3.270236146 + 2.833333334 Combine like terms: 3.270236146 + 2.833333334 = 6.10356948 x = 6.10356948 Simplifying x = 6.10356948Subproblem 2
x + -2.833333334 = -3.270236146 Simplifying x + -2.833333334 = -3.270236146 Reorder the terms: -2.833333334 + x = -3.270236146 Solving -2.833333334 + x = -3.270236146 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 = -3.270236146 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -3.270236146 + 2.833333334 x = -3.270236146 + 2.833333334 Combine like terms: -3.270236146 + 2.833333334 = -0.436902812 x = -0.436902812 Simplifying x = -0.436902812Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.10356948, -0.436902812}Solution
x = {6.10356948, -0.436902812}
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