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Simplifying x(x + 1) = 323 Reorder the terms: x(1 + x) = 323 (1 * x + x * x) = 323 (1x + x2) = 323 Solving 1x + x2 = 323 Solving for variable 'x'. Reorder the terms: -323 + 1x + x2 = 323 + -323 Combine like terms: 323 + -323 = 0 -323 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '323' to each side of the equation. -323 + 1x + 323 + x2 = 0 + 323 Reorder the terms: -323 + 323 + 1x + x2 = 0 + 323 Combine like terms: -323 + 323 = 0 0 + 1x + x2 = 0 + 323 1x + x2 = 0 + 323 Combine like terms: 0 + 323 = 323 1x + x2 = 323 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 = 323 + 0.25 Reorder the terms: 0.25 + x + x2 = 323 + 0.25 Combine like terms: 323 + 0.25 = 323.25 0.25 + x + x2 = 323.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 323.25 Calculate the square root of the right side: 17.979154596 Break this problem into two subproblems by setting (x + 0.5) equal to 17.979154596 and -17.979154596.Subproblem 1
x + 0.5 = 17.979154596 Simplifying x + 0.5 = 17.979154596 Reorder the terms: 0.5 + x = 17.979154596 Solving 0.5 + x = 17.979154596 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 = 17.979154596 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 17.979154596 + -0.5 x = 17.979154596 + -0.5 Combine like terms: 17.979154596 + -0.5 = 17.479154596 x = 17.479154596 Simplifying x = 17.479154596Subproblem 2
x + 0.5 = -17.979154596 Simplifying x + 0.5 = -17.979154596 Reorder the terms: 0.5 + x = -17.979154596 Solving 0.5 + x = -17.979154596 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 = -17.979154596 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -17.979154596 + -0.5 x = -17.979154596 + -0.5 Combine like terms: -17.979154596 + -0.5 = -18.479154596 x = -18.479154596 Simplifying x = -18.479154596Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.479154596, -18.479154596}
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