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Simplifying x(3x + -11) = 44 Reorder the terms: x(-11 + 3x) = 44 (-11 * x + 3x * x) = 44 (-11x + 3x2) = 44 Solving -11x + 3x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + -11x + 3x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14.66666667 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '14.66666667' to each side of the equation. -14.66666667 + -3.666666667x + 14.66666667 + x2 = 0 + 14.66666667 Reorder the terms: -14.66666667 + 14.66666667 + -3.666666667x + x2 = 0 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + -3.666666667x + x2 = 0 + 14.66666667 -3.666666667x + x2 = 0 + 14.66666667 Combine like terms: 0 + 14.66666667 = 14.66666667 -3.666666667x + x2 = 14.66666667 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 = 14.66666667 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 14.66666667 + 3.361111114 Combine like terms: 14.66666667 + 3.361111114 = 18.027777784 3.361111114 + -3.666666667x + x2 = 18.027777784 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 18.027777784 Calculate the square root of the right side: 4.245913068 Break this problem into two subproblems by setting (x + -1.833333334) equal to 4.245913068 and -4.245913068.Subproblem 1
x + -1.833333334 = 4.245913068 Simplifying x + -1.833333334 = 4.245913068 Reorder the terms: -1.833333334 + x = 4.245913068 Solving -1.833333334 + x = 4.245913068 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 = 4.245913068 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 4.245913068 + 1.833333334 x = 4.245913068 + 1.833333334 Combine like terms: 4.245913068 + 1.833333334 = 6.079246402 x = 6.079246402 Simplifying x = 6.079246402Subproblem 2
x + -1.833333334 = -4.245913068 Simplifying x + -1.833333334 = -4.245913068 Reorder the terms: -1.833333334 + x = -4.245913068 Solving -1.833333334 + x = -4.245913068 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 = -4.245913068 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -4.245913068 + 1.833333334 x = -4.245913068 + 1.833333334 Combine like terms: -4.245913068 + 1.833333334 = -2.412579734 x = -2.412579734 Simplifying x = -2.412579734Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.079246402, -2.412579734}
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