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Simplifying (2x + 1)(x + 5) = -3 Reorder the terms: (1 + 2x)(x + 5) = -3 Reorder the terms: (1 + 2x)(5 + x) = -3 Multiply (1 + 2x) * (5 + x) (1(5 + x) + 2x * (5 + x)) = -3 ((5 * 1 + x * 1) + 2x * (5 + x)) = -3 ((5 + 1x) + 2x * (5 + x)) = -3 (5 + 1x + (5 * 2x + x * 2x)) = -3 (5 + 1x + (10x + 2x2)) = -3 Combine like terms: 1x + 10x = 11x (5 + 11x + 2x2) = -3 Solving 5 + 11x + 2x2 = -3 Solving for variable 'x'. Reorder the terms: 5 + 3 + 11x + 2x2 = -3 + 3 Combine like terms: 5 + 3 = 8 8 + 11x + 2x2 = -3 + 3 Combine like terms: -3 + 3 = 0 8 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + 5.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 5.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 5.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5.5x + x2 = 0 + -4 5.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 5.5x + x2 = -4 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -4 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -4 + 7.5625 Combine like terms: -4 + 7.5625 = 3.5625 7.5625 + 5.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + 2.75) equal to 1.887458609 and -1.887458609.Subproblem 1
x + 2.75 = 1.887458609 Simplifying x + 2.75 = 1.887458609 Reorder the terms: 2.75 + x = 1.887458609 Solving 2.75 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 1.887458609 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 1.887458609 + -2.75 x = 1.887458609 + -2.75 Combine like terms: 1.887458609 + -2.75 = -0.862541391 x = -0.862541391 Simplifying x = -0.862541391Subproblem 2
x + 2.75 = -1.887458609 Simplifying x + 2.75 = -1.887458609 Reorder the terms: 2.75 + x = -1.887458609 Solving 2.75 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -1.887458609 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -1.887458609 + -2.75 x = -1.887458609 + -2.75 Combine like terms: -1.887458609 + -2.75 = -4.637458609 x = -4.637458609 Simplifying x = -4.637458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.862541391, -4.637458609}
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