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Simplifying -3x(x + 1) = 8x + -47 Reorder the terms: -3x(1 + x) = 8x + -47 (1 * -3x + x * -3x) = 8x + -47 (-3x + -3x2) = 8x + -47 Reorder the terms: -3x + -3x2 = -47 + 8x Solving -3x + -3x2 = -47 + 8x Solving for variable 'x'. Reorder the terms: 47 + -3x + -8x + -3x2 = -47 + 8x + 47 + -8x Combine like terms: -3x + -8x = -11x 47 + -11x + -3x2 = -47 + 8x + 47 + -8x Reorder the terms: 47 + -11x + -3x2 = -47 + 47 + 8x + -8x Combine like terms: -47 + 47 = 0 47 + -11x + -3x2 = 0 + 8x + -8x 47 + -11x + -3x2 = 8x + -8x Combine like terms: 8x + -8x = 0 47 + -11x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -15.66666667 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '15.66666667' to each side of the equation. -15.66666667 + 3.666666667x + 15.66666667 + x2 = 0 + 15.66666667 Reorder the terms: -15.66666667 + 15.66666667 + 3.666666667x + x2 = 0 + 15.66666667 Combine like terms: -15.66666667 + 15.66666667 = 0.00000000 0.00000000 + 3.666666667x + x2 = 0 + 15.66666667 3.666666667x + x2 = 0 + 15.66666667 Combine like terms: 0 + 15.66666667 = 15.66666667 3.666666667x + x2 = 15.66666667 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 = 15.66666667 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = 15.66666667 + 3.361111114 Combine like terms: 15.66666667 + 3.361111114 = 19.027777784 3.361111114 + 3.666666667x + x2 = 19.027777784 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 19.027777784 Calculate the square root of the right side: 4.36208411 Break this problem into two subproblems by setting (x + 1.833333334) equal to 4.36208411 and -4.36208411.Subproblem 1
x + 1.833333334 = 4.36208411 Simplifying x + 1.833333334 = 4.36208411 Reorder the terms: 1.833333334 + x = 4.36208411 Solving 1.833333334 + x = 4.36208411 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 = 4.36208411 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 4.36208411 + -1.833333334 x = 4.36208411 + -1.833333334 Combine like terms: 4.36208411 + -1.833333334 = 2.528750776 x = 2.528750776 Simplifying x = 2.528750776Subproblem 2
x + 1.833333334 = -4.36208411 Simplifying x + 1.833333334 = -4.36208411 Reorder the terms: 1.833333334 + x = -4.36208411 Solving 1.833333334 + x = -4.36208411 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 = -4.36208411 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -4.36208411 + -1.833333334 x = -4.36208411 + -1.833333334 Combine like terms: -4.36208411 + -1.833333334 = -6.195417444 x = -6.195417444 Simplifying x = -6.195417444Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.528750776, -6.195417444}
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