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Simplifying (2x + 5)(2x + 1) = 3(x + 1)(x + 1) Reorder the terms: (5 + 2x)(2x + 1) = 3(x + 1)(x + 1) Reorder the terms: (5 + 2x)(1 + 2x) = 3(x + 1)(x + 1) Multiply (5 + 2x) * (1 + 2x) (5(1 + 2x) + 2x * (1 + 2x)) = 3(x + 1)(x + 1) ((1 * 5 + 2x * 5) + 2x * (1 + 2x)) = 3(x + 1)(x + 1) ((5 + 10x) + 2x * (1 + 2x)) = 3(x + 1)(x + 1) (5 + 10x + (1 * 2x + 2x * 2x)) = 3(x + 1)(x + 1) (5 + 10x + (2x + 4x2)) = 3(x + 1)(x + 1) Combine like terms: 10x + 2x = 12x (5 + 12x + 4x2) = 3(x + 1)(x + 1) Reorder the terms: 5 + 12x + 4x2 = 3(1 + x)(x + 1) Reorder the terms: 5 + 12x + 4x2 = 3(1 + x)(1 + x) Multiply (1 + x) * (1 + x) 5 + 12x + 4x2 = 3(1(1 + x) + x(1 + x)) 5 + 12x + 4x2 = 3((1 * 1 + x * 1) + x(1 + x)) 5 + 12x + 4x2 = 3((1 + 1x) + x(1 + x)) 5 + 12x + 4x2 = 3(1 + 1x + (1 * x + x * x)) 5 + 12x + 4x2 = 3(1 + 1x + (1x + x2)) Combine like terms: 1x + 1x = 2x 5 + 12x + 4x2 = 3(1 + 2x + x2) 5 + 12x + 4x2 = (1 * 3 + 2x * 3 + x2 * 3) 5 + 12x + 4x2 = (3 + 6x + 3x2) Solving 5 + 12x + 4x2 = 3 + 6x + 3x2 Solving for variable 'x'. Reorder the terms: 5 + -3 + 12x + -6x + 4x2 + -3x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2 Combine like terms: 5 + -3 = 2 2 + 12x + -6x + 4x2 + -3x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2 Combine like terms: 12x + -6x = 6x 2 + 6x + 4x2 + -3x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 2 + 6x + 1x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2 Reorder the terms: 2 + 6x + 1x2 = 3 + -3 + 6x + -6x + 3x2 + -3x2 Combine like terms: 3 + -3 = 0 2 + 6x + 1x2 = 0 + 6x + -6x + 3x2 + -3x2 2 + 6x + 1x2 = 6x + -6x + 3x2 + -3x2 Combine like terms: 6x + -6x = 0 2 + 6x + 1x2 = 0 + 3x2 + -3x2 2 + 6x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 2 + 6x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 6x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 6x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6x + x2 = 0 + -2 6x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 6x + x2 = -2 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -2 + 9 Reorder the terms: 9 + 6x + x2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + 6x + x2 = 7 Factor a perfect square on the left side: (x + 3)(x + 3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 3) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 3 = 2.645751311 Simplifying x + 3 = 2.645751311 Reorder the terms: 3 + x = 2.645751311 Solving 3 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.645751311 + -3 x = 2.645751311 + -3 Combine like terms: 2.645751311 + -3 = -0.354248689 x = -0.354248689 Simplifying x = -0.354248689Subproblem 2
x + 3 = -2.645751311 Simplifying x + 3 = -2.645751311 Reorder the terms: 3 + x = -2.645751311 Solving 3 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.645751311 + -3 x = -2.645751311 + -3 Combine like terms: -2.645751311 + -3 = -5.645751311 x = -5.645751311 Simplifying x = -5.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.354248689, -5.645751311}
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