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Simplifying 2x(3x + -17) = 98 Reorder the terms: 2x(-17 + 3x) = 98 (-17 * 2x + 3x * 2x) = 98 (-34x + 6x2) = 98 Solving -34x + 6x2 = 98 Solving for variable 'x'. Reorder the terms: -98 + -34x + 6x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + -34x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + -17x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-49 + -17x + 3x2)' equal to zero and attempt to solve: Simplifying -49 + -17x + 3x2 = 0 Solving -49 + -17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.33333333 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '16.33333333' to each side of the equation. -16.33333333 + -5.666666667x + 16.33333333 + x2 = 0 + 16.33333333 Reorder the terms: -16.33333333 + 16.33333333 + -5.666666667x + x2 = 0 + 16.33333333 Combine like terms: -16.33333333 + 16.33333333 = 0.00000000 0.00000000 + -5.666666667x + x2 = 0 + 16.33333333 -5.666666667x + x2 = 0 + 16.33333333 Combine like terms: 0 + 16.33333333 = 16.33333333 -5.666666667x + x2 = 16.33333333 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 = 16.33333333 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 16.33333333 + 8.027777782 Combine like terms: 16.33333333 + 8.027777782 = 24.361111112 8.027777782 + -5.666666667x + x2 = 24.361111112 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 24.361111112 Calculate the square root of the right side: 4.935697632 Break this problem into two subproblems by setting (x + -2.833333334) equal to 4.935697632 and -4.935697632.Subproblem 1
x + -2.833333334 = 4.935697632 Simplifying x + -2.833333334 = 4.935697632 Reorder the terms: -2.833333334 + x = 4.935697632 Solving -2.833333334 + x = 4.935697632 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 = 4.935697632 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 4.935697632 + 2.833333334 x = 4.935697632 + 2.833333334 Combine like terms: 4.935697632 + 2.833333334 = 7.769030966 x = 7.769030966 Simplifying x = 7.769030966Subproblem 2
x + -2.833333334 = -4.935697632 Simplifying x + -2.833333334 = -4.935697632 Reorder the terms: -2.833333334 + x = -4.935697632 Solving -2.833333334 + x = -4.935697632 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 = -4.935697632 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -4.935697632 + 2.833333334 x = -4.935697632 + 2.833333334 Combine like terms: -4.935697632 + 2.833333334 = -2.102364298 x = -2.102364298 Simplifying x = -2.102364298Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.769030966, -2.102364298}Solution
x = {7.769030966, -2.102364298}
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