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Simplifying (x + 3)(x + 5) = 25 Reorder the terms: (3 + x)(x + 5) = 25 Reorder the terms: (3 + x)(5 + x) = 25 Multiply (3 + x) * (5 + x) (3(5 + x) + x(5 + x)) = 25 ((5 * 3 + x * 3) + x(5 + x)) = 25 ((15 + 3x) + x(5 + x)) = 25 (15 + 3x + (5 * x + x * x)) = 25 (15 + 3x + (5x + x2)) = 25 Combine like terms: 3x + 5x = 8x (15 + 8x + x2) = 25 Solving 15 + 8x + x2 = 25 Solving for variable 'x'. Reorder the terms: 15 + -25 + 8x + x2 = 25 + -25 Combine like terms: 15 + -25 = -10 -10 + 8x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -10 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 8x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 8x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 8x + x2 = 0 + 10 8x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 8x + x2 = 10 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 = 10 + 16 Reorder the terms: 16 + 8x + x2 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + 8x + x2 = 26 Factor a perfect square on the left side: (x + 4)(x + 4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + 4) equal to 5.099019514 and -5.099019514.Subproblem 1
x + 4 = 5.099019514 Simplifying x + 4 = 5.099019514 Reorder the terms: 4 + x = 5.099019514 Solving 4 + x = 5.099019514 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 = 5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.099019514 + -4 x = 5.099019514 + -4 Combine like terms: 5.099019514 + -4 = 1.099019514 x = 1.099019514 Simplifying x = 1.099019514Subproblem 2
x + 4 = -5.099019514 Simplifying x + 4 = -5.099019514 Reorder the terms: 4 + x = -5.099019514 Solving 4 + x = -5.099019514 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 = -5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.099019514 + -4 x = -5.099019514 + -4 Combine like terms: -5.099019514 + -4 = -9.099019514 x = -9.099019514 Simplifying x = -9.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.099019514, -9.099019514}
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