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Simplifying (3x + -1)(x + 5) = 30 Reorder the terms: (-1 + 3x)(x + 5) = 30 Reorder the terms: (-1 + 3x)(5 + x) = 30 Multiply (-1 + 3x) * (5 + x) (-1(5 + x) + 3x * (5 + x)) = 30 ((5 * -1 + x * -1) + 3x * (5 + x)) = 30 ((-5 + -1x) + 3x * (5 + x)) = 30 (-5 + -1x + (5 * 3x + x * 3x)) = 30 (-5 + -1x + (15x + 3x2)) = 30 Combine like terms: -1x + 15x = 14x (-5 + 14x + 3x2) = 30 Solving -5 + 14x + 3x2 = 30 Solving for variable 'x'. Reorder the terms: -5 + -30 + 14x + 3x2 = 30 + -30 Combine like terms: -5 + -30 = -35 -35 + 14x + 3x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -35 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11.66666667 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + 4.666666667x + 11.66666667 + x2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + 4.666666667x + x2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + 4.666666667x + x2 = 0 + 11.66666667 4.666666667x + x2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 4.666666667x + x2 = 11.66666667 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = 11.66666667 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 11.66666667 + 5.444444448 Combine like terms: 11.66666667 + 5.444444448 = 17.111111118 5.444444448 + 4.666666667x + x2 = 17.111111118 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 17.111111118 Calculate the square root of the right side: 4.136557883 Break this problem into two subproblems by setting (x + 2.333333334) equal to 4.136557883 and -4.136557883.Subproblem 1
x + 2.333333334 = 4.136557883 Simplifying x + 2.333333334 = 4.136557883 Reorder the terms: 2.333333334 + x = 4.136557883 Solving 2.333333334 + x = 4.136557883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 4.136557883 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 4.136557883 + -2.333333334 x = 4.136557883 + -2.333333334 Combine like terms: 4.136557883 + -2.333333334 = 1.803224549 x = 1.803224549 Simplifying x = 1.803224549Subproblem 2
x + 2.333333334 = -4.136557883 Simplifying x + 2.333333334 = -4.136557883 Reorder the terms: 2.333333334 + x = -4.136557883 Solving 2.333333334 + x = -4.136557883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -4.136557883 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -4.136557883 + -2.333333334 x = -4.136557883 + -2.333333334 Combine like terms: -4.136557883 + -2.333333334 = -6.469891217 x = -6.469891217 Simplifying x = -6.469891217Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.803224549, -6.469891217}
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