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Simplifying (3x + 5)(x + -6) = 5x + 10 Reorder the terms: (5 + 3x)(x + -6) = 5x + 10 Reorder the terms: (5 + 3x)(-6 + x) = 5x + 10 Multiply (5 + 3x) * (-6 + x) (5(-6 + x) + 3x * (-6 + x)) = 5x + 10 ((-6 * 5 + x * 5) + 3x * (-6 + x)) = 5x + 10 ((-30 + 5x) + 3x * (-6 + x)) = 5x + 10 (-30 + 5x + (-6 * 3x + x * 3x)) = 5x + 10 (-30 + 5x + (-18x + 3x2)) = 5x + 10 Combine like terms: 5x + -18x = -13x (-30 + -13x + 3x2) = 5x + 10 Reorder the terms: -30 + -13x + 3x2 = 10 + 5x Solving -30 + -13x + 3x2 = 10 + 5x Solving for variable 'x'. Reorder the terms: -30 + -10 + -13x + -5x + 3x2 = 10 + 5x + -10 + -5x Combine like terms: -30 + -10 = -40 -40 + -13x + -5x + 3x2 = 10 + 5x + -10 + -5x Combine like terms: -13x + -5x = -18x -40 + -18x + 3x2 = 10 + 5x + -10 + -5x Reorder the terms: -40 + -18x + 3x2 = 10 + -10 + 5x + -5x Combine like terms: 10 + -10 = 0 -40 + -18x + 3x2 = 0 + 5x + -5x -40 + -18x + 3x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -40 + -18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.33333333 + -6x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -6x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -6x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -6x + x2 = 0 + 13.33333333 -6x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -6x + x2 = 13.33333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 13.33333333 + 9 Reorder the terms: 9 + -6x + x2 = 13.33333333 + 9 Combine like terms: 13.33333333 + 9 = 22.33333333 9 + -6x + x2 = 22.33333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 22.33333333 Calculate the square root of the right side: 4.725815626 Break this problem into two subproblems by setting (x + -3) equal to 4.725815626 and -4.725815626.Subproblem 1
x + -3 = 4.725815626 Simplifying x + -3 = 4.725815626 Reorder the terms: -3 + x = 4.725815626 Solving -3 + x = 4.725815626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.725815626 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.725815626 + 3 x = 4.725815626 + 3 Combine like terms: 4.725815626 + 3 = 7.725815626 x = 7.725815626 Simplifying x = 7.725815626Subproblem 2
x + -3 = -4.725815626 Simplifying x + -3 = -4.725815626 Reorder the terms: -3 + x = -4.725815626 Solving -3 + x = -4.725815626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.725815626 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.725815626 + 3 x = -4.725815626 + 3 Combine like terms: -4.725815626 + 3 = -1.725815626 x = -1.725815626 Simplifying x = -1.725815626Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.725815626, -1.725815626}
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