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Simplifying 3x2 + 17x = 48 Reorder the terms: 17x + 3x2 = 48 Solving 17x + 3x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + 17x + 3x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 5.666666667x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 5.666666667x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 5.666666667x + x2 = 0 + 16 5.666666667x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 5.666666667x + x2 = 16 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 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 16 + 8.027777782 Combine like terms: 16 + 8.027777782 = 24.027777782 8.027777782 + 5.666666667x + x2 = 24.027777782 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 24.027777782 Calculate the square root of the right side: 4.901813724 Break this problem into two subproblems by setting (x + 2.833333334) equal to 4.901813724 and -4.901813724.Subproblem 1
x + 2.833333334 = 4.901813724 Simplifying x + 2.833333334 = 4.901813724 Reorder the terms: 2.833333334 + x = 4.901813724 Solving 2.833333334 + x = 4.901813724 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 = 4.901813724 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 4.901813724 + -2.833333334 x = 4.901813724 + -2.833333334 Combine like terms: 4.901813724 + -2.833333334 = 2.06848039 x = 2.06848039 Simplifying x = 2.06848039Subproblem 2
x + 2.833333334 = -4.901813724 Simplifying x + 2.833333334 = -4.901813724 Reorder the terms: 2.833333334 + x = -4.901813724 Solving 2.833333334 + x = -4.901813724 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 = -4.901813724 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -4.901813724 + -2.833333334 x = -4.901813724 + -2.833333334 Combine like terms: -4.901813724 + -2.833333334 = -7.735147058 x = -7.735147058 Simplifying x = -7.735147058Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.06848039, -7.735147058}
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