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Simplifying (x)(x + 1) = 7920 Reorder the terms: x(1 + x) = 7920 (1 * x + x * x) = 7920 (1x + x2) = 7920 Solving 1x + x2 = 7920 Solving for variable 'x'. Reorder the terms: -7920 + 1x + x2 = 7920 + -7920 Combine like terms: 7920 + -7920 = 0 -7920 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7920' to each side of the equation. -7920 + 1x + 7920 + x2 = 0 + 7920 Reorder the terms: -7920 + 7920 + 1x + x2 = 0 + 7920 Combine like terms: -7920 + 7920 = 0 0 + 1x + x2 = 0 + 7920 1x + x2 = 0 + 7920 Combine like terms: 0 + 7920 = 7920 1x + x2 = 7920 The x term is 1x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 7920 + 0.25 Reorder the terms: 0.25 + x + x2 = 7920 + 0.25 Combine like terms: 7920 + 0.25 = 7920.25 0.25 + x + x2 = 7920.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7920.25 Calculate the square root of the right side: 88.995786417 Break this problem into two subproblems by setting (x + 0.5) equal to 88.995786417 and -88.995786417.Subproblem 1
x + 0.5 = 88.995786417 Simplifying x + 0.5 = 88.995786417 Reorder the terms: 0.5 + x = 88.995786417 Solving 0.5 + x = 88.995786417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 88.995786417 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 88.995786417 + -0.5 x = 88.995786417 + -0.5 Combine like terms: 88.995786417 + -0.5 = 88.495786417 x = 88.495786417 Simplifying x = 88.495786417Subproblem 2
x + 0.5 = -88.995786417 Simplifying x + 0.5 = -88.995786417 Reorder the terms: 0.5 + x = -88.995786417 Solving 0.5 + x = -88.995786417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -88.995786417 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -88.995786417 + -0.5 x = -88.995786417 + -0.5 Combine like terms: -88.995786417 + -0.5 = -89.495786417 x = -89.495786417 Simplifying x = -89.495786417Solution
The solution to the problem is based on the solutions from the subproblems. x = {88.495786417, -89.495786417}
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