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Simplifying 4x(2x + 3) = 3(2x + 5) + 2 Reorder the terms: 4x(3 + 2x) = 3(2x + 5) + 2 (3 * 4x + 2x * 4x) = 3(2x + 5) + 2 (12x + 8x2) = 3(2x + 5) + 2 Reorder the terms: 12x + 8x2 = 3(5 + 2x) + 2 12x + 8x2 = (5 * 3 + 2x * 3) + 2 12x + 8x2 = (15 + 6x) + 2 Reorder the terms: 12x + 8x2 = 15 + 2 + 6x Combine like terms: 15 + 2 = 17 12x + 8x2 = 17 + 6x Solving 12x + 8x2 = 17 + 6x Solving for variable 'x'. Reorder the terms: -17 + 12x + -6x + 8x2 = 17 + 6x + -17 + -6x Combine like terms: 12x + -6x = 6x -17 + 6x + 8x2 = 17 + 6x + -17 + -6x Reorder the terms: -17 + 6x + 8x2 = 17 + -17 + 6x + -6x Combine like terms: 17 + -17 = 0 -17 + 6x + 8x2 = 0 + 6x + -6x -17 + 6x + 8x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -17 + 6x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.125 + 0.75x + x2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + 0.75x + 2.125 + x2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + 0.75x + x2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + 0.75x + x2 = 0 + 2.125 0.75x + x2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 0.75x + x2 = 2.125 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 2.125 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 2.125 + 0.140625 Combine like terms: 2.125 + 0.140625 = 2.265625 0.140625 + 0.75x + x2 = 2.265625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + 0.375) equal to 1.505199322 and -1.505199322.Subproblem 1
x + 0.375 = 1.505199322 Simplifying x + 0.375 = 1.505199322 Reorder the terms: 0.375 + x = 1.505199322 Solving 0.375 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 1.505199322 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.505199322 + -0.375 x = 1.505199322 + -0.375 Combine like terms: 1.505199322 + -0.375 = 1.130199322 x = 1.130199322 Simplifying x = 1.130199322Subproblem 2
x + 0.375 = -1.505199322 Simplifying x + 0.375 = -1.505199322 Reorder the terms: 0.375 + x = -1.505199322 Solving 0.375 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -1.505199322 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.505199322 + -0.375 x = -1.505199322 + -0.375 Combine like terms: -1.505199322 + -0.375 = -1.880199322 x = -1.880199322 Simplifying x = -1.880199322Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.130199322, -1.880199322}
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