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Simplifying (x + 1)(x + 2) = 117649 Reorder the terms: (1 + x)(x + 2) = 117649 Reorder the terms: (1 + x)(2 + x) = 117649 Multiply (1 + x) * (2 + x) (1(2 + x) + x(2 + x)) = 117649 ((2 * 1 + x * 1) + x(2 + x)) = 117649 ((2 + 1x) + x(2 + x)) = 117649 (2 + 1x + (2 * x + x * x)) = 117649 (2 + 1x + (2x + x2)) = 117649 Combine like terms: 1x + 2x = 3x (2 + 3x + x2) = 117649 Solving 2 + 3x + x2 = 117649 Solving for variable 'x'. Reorder the terms: 2 + -117649 + 3x + x2 = 117649 + -117649 Combine like terms: 2 + -117649 = -117647 -117647 + 3x + x2 = 117649 + -117649 Combine like terms: 117649 + -117649 = 0 -117647 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '117647' to each side of the equation. -117647 + 3x + 117647 + x2 = 0 + 117647 Reorder the terms: -117647 + 117647 + 3x + x2 = 0 + 117647 Combine like terms: -117647 + 117647 = 0 0 + 3x + x2 = 0 + 117647 3x + x2 = 0 + 117647 Combine like terms: 0 + 117647 = 117647 3x + x2 = 117647 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 117647 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 117647 + 2.25 Combine like terms: 117647 + 2.25 = 117649.25 2.25 + 3x + x2 = 117649.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 117649.25 Calculate the square root of the right side: 343.000364431 Break this problem into two subproblems by setting (x + 1.5) equal to 343.000364431 and -343.000364431.Subproblem 1
x + 1.5 = 343.000364431 Simplifying x + 1.5 = 343.000364431 Reorder the terms: 1.5 + x = 343.000364431 Solving 1.5 + x = 343.000364431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 343.000364431 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 343.000364431 + -1.5 x = 343.000364431 + -1.5 Combine like terms: 343.000364431 + -1.5 = 341.500364431 x = 341.500364431 Simplifying x = 341.500364431Subproblem 2
x + 1.5 = -343.000364431 Simplifying x + 1.5 = -343.000364431 Reorder the terms: 1.5 + x = -343.000364431 Solving 1.5 + x = -343.000364431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -343.000364431 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -343.000364431 + -1.5 x = -343.000364431 + -1.5 Combine like terms: -343.000364431 + -1.5 = -344.500364431 x = -344.500364431 Simplifying x = -344.500364431Solution
The solution to the problem is based on the solutions from the subproblems. x = {341.500364431, -344.500364431}
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