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Simplifying (x + 3)(x + 8) = 30 Reorder the terms: (3 + x)(x + 8) = 30 Reorder the terms: (3 + x)(8 + x) = 30 Multiply (3 + x) * (8 + x) (3(8 + x) + x(8 + x)) = 30 ((8 * 3 + x * 3) + x(8 + x)) = 30 ((24 + 3x) + x(8 + x)) = 30 (24 + 3x + (8 * x + x * x)) = 30 (24 + 3x + (8x + x2)) = 30 Combine like terms: 3x + 8x = 11x (24 + 11x + x2) = 30 Solving 24 + 11x + x2 = 30 Solving for variable 'x'. Reorder the terms: 24 + -30 + 11x + x2 = 30 + -30 Combine like terms: 24 + -30 = -6 -6 + 11x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -6 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 11x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 11x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 11x + x2 = 0 + 6 11x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 11x + x2 = 6 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 6 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 6 + 30.25 Combine like terms: 6 + 30.25 = 36.25 30.25 + 11x + x2 = 36.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + 5.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + 5.5 = 6.020797289 Simplifying x + 5.5 = 6.020797289 Reorder the terms: 5.5 + x = 6.020797289 Solving 5.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 6.020797289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.020797289 + -5.5 x = 6.020797289 + -5.5 Combine like terms: 6.020797289 + -5.5 = 0.520797289 x = 0.520797289 Simplifying x = 0.520797289Subproblem 2
x + 5.5 = -6.020797289 Simplifying x + 5.5 = -6.020797289 Reorder the terms: 5.5 + x = -6.020797289 Solving 5.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -6.020797289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.020797289 + -5.5 x = -6.020797289 + -5.5 Combine like terms: -6.020797289 + -5.5 = -11.520797289 x = -11.520797289 Simplifying x = -11.520797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.520797289, -11.520797289}
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