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Simplifying (2x + 4)(x + 2) = 77 Reorder the terms: (4 + 2x)(x + 2) = 77 Reorder the terms: (4 + 2x)(2 + x) = 77 Multiply (4 + 2x) * (2 + x) (4(2 + x) + 2x * (2 + x)) = 77 ((2 * 4 + x * 4) + 2x * (2 + x)) = 77 ((8 + 4x) + 2x * (2 + x)) = 77 (8 + 4x + (2 * 2x + x * 2x)) = 77 (8 + 4x + (4x + 2x2)) = 77 Combine like terms: 4x + 4x = 8x (8 + 8x + 2x2) = 77 Solving 8 + 8x + 2x2 = 77 Solving for variable 'x'. Reorder the terms: 8 + -77 + 8x + 2x2 = 77 + -77 Combine like terms: 8 + -77 = -69 -69 + 8x + 2x2 = 77 + -77 Combine like terms: 77 + -77 = 0 -69 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -34.5 + 4x + x2 = 0 Move the constant term to the right: Add '34.5' to each side of the equation. -34.5 + 4x + 34.5 + x2 = 0 + 34.5 Reorder the terms: -34.5 + 34.5 + 4x + x2 = 0 + 34.5 Combine like terms: -34.5 + 34.5 = 0.0 0.0 + 4x + x2 = 0 + 34.5 4x + x2 = 0 + 34.5 Combine like terms: 0 + 34.5 = 34.5 4x + x2 = 34.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 34.5 + 4 Reorder the terms: 4 + 4x + x2 = 34.5 + 4 Combine like terms: 34.5 + 4 = 38.5 4 + 4x + x2 = 38.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 38.5 Calculate the square root of the right side: 6.204836823 Break this problem into two subproblems by setting (x + 2) equal to 6.204836823 and -6.204836823.Subproblem 1
x + 2 = 6.204836823 Simplifying x + 2 = 6.204836823 Reorder the terms: 2 + x = 6.204836823 Solving 2 + x = 6.204836823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.204836823 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.204836823 + -2 x = 6.204836823 + -2 Combine like terms: 6.204836823 + -2 = 4.204836823 x = 4.204836823 Simplifying x = 4.204836823Subproblem 2
x + 2 = -6.204836823 Simplifying x + 2 = -6.204836823 Reorder the terms: 2 + x = -6.204836823 Solving 2 + x = -6.204836823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.204836823 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.204836823 + -2 x = -6.204836823 + -2 Combine like terms: -6.204836823 + -2 = -8.204836823 x = -8.204836823 Simplifying x = -8.204836823Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.204836823, -8.204836823}
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