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Simplifying (3x + 2)(x + 8) = 88 Reorder the terms: (2 + 3x)(x + 8) = 88 Reorder the terms: (2 + 3x)(8 + x) = 88 Multiply (2 + 3x) * (8 + x) (2(8 + x) + 3x * (8 + x)) = 88 ((8 * 2 + x * 2) + 3x * (8 + x)) = 88 ((16 + 2x) + 3x * (8 + x)) = 88 (16 + 2x + (8 * 3x + x * 3x)) = 88 (16 + 2x + (24x + 3x2)) = 88 Combine like terms: 2x + 24x = 26x (16 + 26x + 3x2) = 88 Solving 16 + 26x + 3x2 = 88 Solving for variable 'x'. Reorder the terms: 16 + -88 + 26x + 3x2 = 88 + -88 Combine like terms: 16 + -88 = -72 -72 + 26x + 3x2 = 88 + -88 Combine like terms: 88 + -88 = 0 -72 + 26x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -24 + 8.666666667x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 8.666666667x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 8.666666667x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 8.666666667x + x2 = 0 + 24 8.666666667x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 8.666666667x + x2 = 24 The x term is 8.666666667x. Take half its coefficient (4.333333334). Square it (18.77777778) and add it to both sides. Add '18.77777778' to each side of the equation. 8.666666667x + 18.77777778 + x2 = 24 + 18.77777778 Reorder the terms: 18.77777778 + 8.666666667x + x2 = 24 + 18.77777778 Combine like terms: 24 + 18.77777778 = 42.77777778 18.77777778 + 8.666666667x + x2 = 42.77777778 Factor a perfect square on the left side: (x + 4.333333334)(x + 4.333333334) = 42.77777778 Calculate the square root of the right side: 6.54047229 Break this problem into two subproblems by setting (x + 4.333333334) equal to 6.54047229 and -6.54047229.Subproblem 1
x + 4.333333334 = 6.54047229 Simplifying x + 4.333333334 = 6.54047229 Reorder the terms: 4.333333334 + x = 6.54047229 Solving 4.333333334 + x = 6.54047229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.333333334' to each side of the equation. 4.333333334 + -4.333333334 + x = 6.54047229 + -4.333333334 Combine like terms: 4.333333334 + -4.333333334 = 0.000000000 0.000000000 + x = 6.54047229 + -4.333333334 x = 6.54047229 + -4.333333334 Combine like terms: 6.54047229 + -4.333333334 = 2.207138956 x = 2.207138956 Simplifying x = 2.207138956Subproblem 2
x + 4.333333334 = -6.54047229 Simplifying x + 4.333333334 = -6.54047229 Reorder the terms: 4.333333334 + x = -6.54047229 Solving 4.333333334 + x = -6.54047229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.333333334' to each side of the equation. 4.333333334 + -4.333333334 + x = -6.54047229 + -4.333333334 Combine like terms: 4.333333334 + -4.333333334 = 0.000000000 0.000000000 + x = -6.54047229 + -4.333333334 x = -6.54047229 + -4.333333334 Combine like terms: -6.54047229 + -4.333333334 = -10.873805624 x = -10.873805624 Simplifying x = -10.873805624Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.207138956, -10.873805624}
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