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Simplifying (x + 5)(4x + 3) = -3 Reorder the terms: (5 + x)(4x + 3) = -3 Reorder the terms: (5 + x)(3 + 4x) = -3 Multiply (5 + x) * (3 + 4x) (5(3 + 4x) + x(3 + 4x)) = -3 ((3 * 5 + 4x * 5) + x(3 + 4x)) = -3 ((15 + 20x) + x(3 + 4x)) = -3 (15 + 20x + (3 * x + 4x * x)) = -3 (15 + 20x + (3x + 4x2)) = -3 Combine like terms: 20x + 3x = 23x (15 + 23x + 4x2) = -3 Solving 15 + 23x + 4x2 = -3 Solving for variable 'x'. Reorder the terms: 15 + 3 + 23x + 4x2 = -3 + 3 Combine like terms: 15 + 3 = 18 18 + 23x + 4x2 = -3 + 3 Combine like terms: -3 + 3 = 0 18 + 23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.5 + 5.75x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 5.75x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 5.75x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 5.75x + x2 = 0 + -4.5 5.75x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 5.75x + x2 = -4.5 The x term is 5.75x. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75x + 8.265625 + x2 = -4.5 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = -4.5 + 8.265625 Combine like terms: -4.5 + 8.265625 = 3.765625 8.265625 + 5.75x + x2 = 3.765625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (x + 2.875) equal to 1.940521837 and -1.940521837.Subproblem 1
x + 2.875 = 1.940521837 Simplifying x + 2.875 = 1.940521837 Reorder the terms: 2.875 + x = 1.940521837 Solving 2.875 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 1.940521837 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 1.940521837 + -2.875 x = 1.940521837 + -2.875 Combine like terms: 1.940521837 + -2.875 = -0.934478163 x = -0.934478163 Simplifying x = -0.934478163Subproblem 2
x + 2.875 = -1.940521837 Simplifying x + 2.875 = -1.940521837 Reorder the terms: 2.875 + x = -1.940521837 Solving 2.875 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -1.940521837 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -1.940521837 + -2.875 x = -1.940521837 + -2.875 Combine like terms: -1.940521837 + -2.875 = -4.815521837 x = -4.815521837 Simplifying x = -4.815521837Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.934478163, -4.815521837}
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