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Simplifying (x + 4)(x + 4) = 44 Reorder the terms: (4 + x)(x + 4) = 44 Reorder the terms: (4 + x)(4 + x) = 44 Multiply (4 + x) * (4 + x) (4(4 + x) + x(4 + x)) = 44 ((4 * 4 + x * 4) + x(4 + x)) = 44 ((16 + 4x) + x(4 + x)) = 44 (16 + 4x + (4 * x + x * x)) = 44 (16 + 4x + (4x + x2)) = 44 Combine like terms: 4x + 4x = 8x (16 + 8x + x2) = 44 Solving 16 + 8x + x2 = 44 Solving for variable 'x'. Reorder the terms: 16 + -44 + 8x + x2 = 44 + -44 Combine like terms: 16 + -44 = -28 -28 + 8x + x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -28 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 8x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 8x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 8x + x2 = 0 + 28 8x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 8x + x2 = 28 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 28 + 16 Reorder the terms: 16 + 8x + x2 = 28 + 16 Combine like terms: 28 + 16 = 44 16 + 8x + x2 = 44 Factor a perfect square on the left side: (x + 4)(x + 4) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + 4) equal to 6.633249581 and -6.633249581.Subproblem 1
x + 4 = 6.633249581 Simplifying x + 4 = 6.633249581 Reorder the terms: 4 + x = 6.633249581 Solving 4 + x = 6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 6.633249581 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.633249581 + -4 x = 6.633249581 + -4 Combine like terms: 6.633249581 + -4 = 2.633249581 x = 2.633249581 Simplifying x = 2.633249581Subproblem 2
x + 4 = -6.633249581 Simplifying x + 4 = -6.633249581 Reorder the terms: 4 + x = -6.633249581 Solving 4 + x = -6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -6.633249581 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.633249581 + -4 x = -6.633249581 + -4 Combine like terms: -6.633249581 + -4 = -10.633249581 x = -10.633249581 Simplifying x = -10.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.633249581, -10.633249581}
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