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Simplifying (4x + 3)(x + 1) = 15 Reorder the terms: (3 + 4x)(x + 1) = 15 Reorder the terms: (3 + 4x)(1 + x) = 15 Multiply (3 + 4x) * (1 + x) (3(1 + x) + 4x * (1 + x)) = 15 ((1 * 3 + x * 3) + 4x * (1 + x)) = 15 ((3 + 3x) + 4x * (1 + x)) = 15 (3 + 3x + (1 * 4x + x * 4x)) = 15 (3 + 3x + (4x + 4x2)) = 15 Combine like terms: 3x + 4x = 7x (3 + 7x + 4x2) = 15 Solving 3 + 7x + 4x2 = 15 Solving for variable 'x'. Reorder the terms: 3 + -15 + 7x + 4x2 = 15 + -15 Combine like terms: 3 + -15 = -12 -12 + 7x + 4x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -12 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + 1.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.75x + x2 = 0 + 3 1.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.75x + x2 = 3 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 3 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 3 + 0.765625 Combine like terms: 3 + 0.765625 = 3.765625 0.765625 + 1.75x + x2 = 3.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (x + 0.875) equal to 1.940521837 and -1.940521837.Subproblem 1
x + 0.875 = 1.940521837 Simplifying x + 0.875 = 1.940521837 Reorder the terms: 0.875 + x = 1.940521837 Solving 0.875 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.940521837 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.940521837 + -0.875 x = 1.940521837 + -0.875 Combine like terms: 1.940521837 + -0.875 = 1.065521837 x = 1.065521837 Simplifying x = 1.065521837Subproblem 2
x + 0.875 = -1.940521837 Simplifying x + 0.875 = -1.940521837 Reorder the terms: 0.875 + x = -1.940521837 Solving 0.875 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.940521837 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.940521837 + -0.875 x = -1.940521837 + -0.875 Combine like terms: -1.940521837 + -0.875 = -2.815521837 x = -2.815521837 Simplifying x = -2.815521837Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.065521837, -2.815521837}
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