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Simplifying 3x2 + 11x = 90 Reorder the terms: 11x + 3x2 = 90 Solving 11x + 3x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 11x + 3x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 3.666666667x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 3.666666667x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 3.666666667x + x2 = 0 + 30 3.666666667x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 3.666666667x + x2 = 30 The x term is 3.666666667x. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667x + 3.361111114 + x2 = 30 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = 30 + 3.361111114 Combine like terms: 30 + 3.361111114 = 33.361111114 3.361111114 + 3.666666667x + x2 = 33.361111114 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 33.361111114 Calculate the square root of the right side: 5.775907817 Break this problem into two subproblems by setting (x + 1.833333334) equal to 5.775907817 and -5.775907817.Subproblem 1
x + 1.833333334 = 5.775907817 Simplifying x + 1.833333334 = 5.775907817 Reorder the terms: 1.833333334 + x = 5.775907817 Solving 1.833333334 + x = 5.775907817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = 5.775907817 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 5.775907817 + -1.833333334 x = 5.775907817 + -1.833333334 Combine like terms: 5.775907817 + -1.833333334 = 3.942574483 x = 3.942574483 Simplifying x = 3.942574483Subproblem 2
x + 1.833333334 = -5.775907817 Simplifying x + 1.833333334 = -5.775907817 Reorder the terms: 1.833333334 + x = -5.775907817 Solving 1.833333334 + x = -5.775907817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = -5.775907817 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -5.775907817 + -1.833333334 x = -5.775907817 + -1.833333334 Combine like terms: -5.775907817 + -1.833333334 = -7.609241151 x = -7.609241151 Simplifying x = -7.609241151Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.942574483, -7.609241151}
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