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Simplifying (4x + 3)(x + 2) = 3 Reorder the terms: (3 + 4x)(x + 2) = 3 Reorder the terms: (3 + 4x)(2 + x) = 3 Multiply (3 + 4x) * (2 + x) (3(2 + x) + 4x * (2 + x)) = 3 ((2 * 3 + x * 3) + 4x * (2 + x)) = 3 ((6 + 3x) + 4x * (2 + x)) = 3 (6 + 3x + (2 * 4x + x * 4x)) = 3 (6 + 3x + (8x + 4x2)) = 3 Combine like terms: 3x + 8x = 11x (6 + 11x + 4x2) = 3 Solving 6 + 11x + 4x2 = 3 Solving for variable 'x'. Reorder the terms: 6 + -3 + 11x + 4x2 = 3 + -3 Combine like terms: 6 + -3 = 3 3 + 11x + 4x2 = 3 + -3 Combine like terms: 3 + -3 = 0 3 + 11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 2.75x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 2.75x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 2.75x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 2.75x + x2 = 0 + -0.75 2.75x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 2.75x + x2 = -0.75 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = -0.75 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = -0.75 + 1.890625 Combine like terms: -0.75 + 1.890625 = 1.140625 1.890625 + 2.75x + x2 = 1.140625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + 1.375) equal to 1.068000468 and -1.068000468.Subproblem 1
x + 1.375 = 1.068000468 Simplifying x + 1.375 = 1.068000468 Reorder the terms: 1.375 + x = 1.068000468 Solving 1.375 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 1.068000468 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 1.068000468 + -1.375 x = 1.068000468 + -1.375 Combine like terms: 1.068000468 + -1.375 = -0.306999532 x = -0.306999532 Simplifying x = -0.306999532Subproblem 2
x + 1.375 = -1.068000468 Simplifying x + 1.375 = -1.068000468 Reorder the terms: 1.375 + x = -1.068000468 Solving 1.375 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -1.068000468 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -1.068000468 + -1.375 x = -1.068000468 + -1.375 Combine like terms: -1.068000468 + -1.375 = -2.443000468 x = -2.443000468 Simplifying x = -2.443000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.306999532, -2.443000468}
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