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Simplifying (8 + x)(4 + x) = 98 Multiply (8 + x) * (4 + x) (8(4 + x) + x(4 + x)) = 98 ((4 * 8 + x * 8) + x(4 + x)) = 98 ((32 + 8x) + x(4 + x)) = 98 (32 + 8x + (4 * x + x * x)) = 98 (32 + 8x + (4x + x2)) = 98 Combine like terms: 8x + 4x = 12x (32 + 12x + x2) = 98 Solving 32 + 12x + x2 = 98 Solving for variable 'x'. Reorder the terms: 32 + -98 + 12x + x2 = 98 + -98 Combine like terms: 32 + -98 = -66 -66 + 12x + x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -66 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 12x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + 12x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 12x + x2 = 0 + 66 12x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 12x + x2 = 66 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 = 66 + 36 Reorder the terms: 36 + 12x + x2 = 66 + 36 Combine like terms: 66 + 36 = 102 36 + 12x + x2 = 102 Factor a perfect square on the left side: (x + 6)(x + 6) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (x + 6) equal to 10.099504938 and -10.099504938.Subproblem 1
x + 6 = 10.099504938 Simplifying x + 6 = 10.099504938 Reorder the terms: 6 + x = 10.099504938 Solving 6 + x = 10.099504938 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 = 10.099504938 + -6 Combine like terms: 6 + -6 = 0 0 + x = 10.099504938 + -6 x = 10.099504938 + -6 Combine like terms: 10.099504938 + -6 = 4.099504938 x = 4.099504938 Simplifying x = 4.099504938Subproblem 2
x + 6 = -10.099504938 Simplifying x + 6 = -10.099504938 Reorder the terms: 6 + x = -10.099504938 Solving 6 + x = -10.099504938 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 = -10.099504938 + -6 Combine like terms: 6 + -6 = 0 0 + x = -10.099504938 + -6 x = -10.099504938 + -6 Combine like terms: -10.099504938 + -6 = -16.099504938 x = -16.099504938 Simplifying x = -16.099504938Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.099504938, -16.099504938}
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