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Simplifying (3 + -1x)(x + 4) + 16 = 12x + -1(x + 3) Reorder the terms: (3 + -1x)(4 + x) + 16 = 12x + -1(x + 3) Multiply (3 + -1x) * (4 + x) (3(4 + x) + -1x * (4 + x)) + 16 = 12x + -1(x + 3) ((4 * 3 + x * 3) + -1x * (4 + x)) + 16 = 12x + -1(x + 3) ((12 + 3x) + -1x * (4 + x)) + 16 = 12x + -1(x + 3) (12 + 3x + (4 * -1x + x * -1x)) + 16 = 12x + -1(x + 3) (12 + 3x + (-4x + -1x2)) + 16 = 12x + -1(x + 3) Combine like terms: 3x + -4x = -1x (12 + -1x + -1x2) + 16 = 12x + -1(x + 3) Reorder the terms: 12 + 16 + -1x + -1x2 = 12x + -1(x + 3) Combine like terms: 12 + 16 = 28 28 + -1x + -1x2 = 12x + -1(x + 3) Reorder the terms: 28 + -1x + -1x2 = 12x + -1(3 + x) 28 + -1x + -1x2 = 12x + (3 * -1 + x * -1) 28 + -1x + -1x2 = 12x + (-3 + -1x) Reorder the terms: 28 + -1x + -1x2 = -3 + 12x + -1x Combine like terms: 12x + -1x = 11x 28 + -1x + -1x2 = -3 + 11x Solving 28 + -1x + -1x2 = -3 + 11x Solving for variable 'x'. Reorder the terms: 28 + 3 + -1x + -11x + -1x2 = -3 + 11x + 3 + -11x Combine like terms: 28 + 3 = 31 31 + -1x + -11x + -1x2 = -3 + 11x + 3 + -11x Combine like terms: -1x + -11x = -12x 31 + -12x + -1x2 = -3 + 11x + 3 + -11x Reorder the terms: 31 + -12x + -1x2 = -3 + 3 + 11x + -11x Combine like terms: -3 + 3 = 0 31 + -12x + -1x2 = 0 + 11x + -11x 31 + -12x + -1x2 = 11x + -11x Combine like terms: 11x + -11x = 0 31 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + 12x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 12x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 12x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 12x + x2 = 0 + 31 12x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 12x + x2 = 31 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 31 + 36 Reorder the terms: 36 + 12x + x2 = 31 + 36 Combine like terms: 31 + 36 = 67 36 + 12x + x2 = 67 Factor a perfect square on the left side: (x + 6)(x + 6) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 6) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 6 = 8.185352772 Simplifying x + 6 = 8.185352772 Reorder the terms: 6 + x = 8.185352772 Solving 6 + x = 8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 8.185352772 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.185352772 + -6 x = 8.185352772 + -6 Combine like terms: 8.185352772 + -6 = 2.185352772 x = 2.185352772 Simplifying x = 2.185352772Subproblem 2
x + 6 = -8.185352772 Simplifying x + 6 = -8.185352772 Reorder the terms: 6 + x = -8.185352772 Solving 6 + x = -8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -8.185352772 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.185352772 + -6 x = -8.185352772 + -6 Combine like terms: -8.185352772 + -6 = -14.185352772 x = -14.185352772 Simplifying x = -14.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.185352772, -14.185352772}
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