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Simplifying (x + 2)(x + 5) = 495 Reorder the terms: (2 + x)(x + 5) = 495 Reorder the terms: (2 + x)(5 + x) = 495 Multiply (2 + x) * (5 + x) (2(5 + x) + x(5 + x)) = 495 ((5 * 2 + x * 2) + x(5 + x)) = 495 ((10 + 2x) + x(5 + x)) = 495 (10 + 2x + (5 * x + x * x)) = 495 (10 + 2x + (5x + x2)) = 495 Combine like terms: 2x + 5x = 7x (10 + 7x + x2) = 495 Solving 10 + 7x + x2 = 495 Solving for variable 'x'. Reorder the terms: 10 + -495 + 7x + x2 = 495 + -495 Combine like terms: 10 + -495 = -485 -485 + 7x + x2 = 495 + -495 Combine like terms: 495 + -495 = 0 -485 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '485' to each side of the equation. -485 + 7x + 485 + x2 = 0 + 485 Reorder the terms: -485 + 485 + 7x + x2 = 0 + 485 Combine like terms: -485 + 485 = 0 0 + 7x + x2 = 0 + 485 7x + x2 = 0 + 485 Combine like terms: 0 + 485 = 485 7x + x2 = 485 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 485 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 485 + 12.25 Combine like terms: 485 + 12.25 = 497.25 12.25 + 7x + x2 = 497.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 497.25 Calculate the square root of the right side: 22.299103121 Break this problem into two subproblems by setting (x + 3.5) equal to 22.299103121 and -22.299103121.Subproblem 1
x + 3.5 = 22.299103121 Simplifying x + 3.5 = 22.299103121 Reorder the terms: 3.5 + x = 22.299103121 Solving 3.5 + x = 22.299103121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 22.299103121 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 22.299103121 + -3.5 x = 22.299103121 + -3.5 Combine like terms: 22.299103121 + -3.5 = 18.799103121 x = 18.799103121 Simplifying x = 18.799103121Subproblem 2
x + 3.5 = -22.299103121 Simplifying x + 3.5 = -22.299103121 Reorder the terms: 3.5 + x = -22.299103121 Solving 3.5 + x = -22.299103121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -22.299103121 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -22.299103121 + -3.5 x = -22.299103121 + -3.5 Combine like terms: -22.299103121 + -3.5 = -25.799103121 x = -25.799103121 Simplifying x = -25.799103121Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.799103121, -25.799103121}
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