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Simplifying (x + 3)(x + 5) = 26 Reorder the terms: (3 + x)(x + 5) = 26 Reorder the terms: (3 + x)(5 + x) = 26 Multiply (3 + x) * (5 + x) (3(5 + x) + x(5 + x)) = 26 ((5 * 3 + x * 3) + x(5 + x)) = 26 ((15 + 3x) + x(5 + x)) = 26 (15 + 3x + (5 * x + x * x)) = 26 (15 + 3x + (5x + x2)) = 26 Combine like terms: 3x + 5x = 8x (15 + 8x + x2) = 26 Solving 15 + 8x + x2 = 26 Solving for variable 'x'. Reorder the terms: 15 + -26 + 8x + x2 = 26 + -26 Combine like terms: 15 + -26 = -11 -11 + 8x + x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -11 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 8x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 8x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 8x + x2 = 0 + 11 8x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 8x + x2 = 11 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 = 11 + 16 Reorder the terms: 16 + 8x + x2 = 11 + 16 Combine like terms: 11 + 16 = 27 16 + 8x + x2 = 27 Factor a perfect square on the left side: (x + 4)(x + 4) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + 4) equal to 5.196152423 and -5.196152423.Subproblem 1
x + 4 = 5.196152423 Simplifying x + 4 = 5.196152423 Reorder the terms: 4 + x = 5.196152423 Solving 4 + x = 5.196152423 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 = 5.196152423 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.196152423 + -4 x = 5.196152423 + -4 Combine like terms: 5.196152423 + -4 = 1.196152423 x = 1.196152423 Simplifying x = 1.196152423Subproblem 2
x + 4 = -5.196152423 Simplifying x + 4 = -5.196152423 Reorder the terms: 4 + x = -5.196152423 Solving 4 + x = -5.196152423 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 = -5.196152423 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.196152423 + -4 x = -5.196152423 + -4 Combine like terms: -5.196152423 + -4 = -9.196152423 x = -9.196152423 Simplifying x = -9.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.196152423, -9.196152423}
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