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Simplifying 3x2 + 11x + -45 = 0 Reorder the terms: -45 + 11x + 3x2 = 0 Solving -45 + 11x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -15 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 3.666666667x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 3.666666667x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 3.666666667x + x2 = 0 + 15 3.666666667x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 3.666666667x + x2 = 15 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 = 15 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = 15 + 3.361111114 Combine like terms: 15 + 3.361111114 = 18.361111114 3.361111114 + 3.666666667x + x2 = 18.361111114 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 18.361111114 Calculate the square root of the right side: 4.284986711 Break this problem into two subproblems by setting (x + 1.833333334) equal to 4.284986711 and -4.284986711.Subproblem 1
x + 1.833333334 = 4.284986711 Simplifying x + 1.833333334 = 4.284986711 Reorder the terms: 1.833333334 + x = 4.284986711 Solving 1.833333334 + x = 4.284986711 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 = 4.284986711 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 4.284986711 + -1.833333334 x = 4.284986711 + -1.833333334 Combine like terms: 4.284986711 + -1.833333334 = 2.451653377 x = 2.451653377 Simplifying x = 2.451653377Subproblem 2
x + 1.833333334 = -4.284986711 Simplifying x + 1.833333334 = -4.284986711 Reorder the terms: 1.833333334 + x = -4.284986711 Solving 1.833333334 + x = -4.284986711 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 = -4.284986711 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -4.284986711 + -1.833333334 x = -4.284986711 + -1.833333334 Combine like terms: -4.284986711 + -1.833333334 = -6.118320045 x = -6.118320045 Simplifying x = -6.118320045Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.451653377, -6.118320045}
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