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Simplifying 1125 = n(n + -3) Reorder the terms: 1125 = n(-3 + n) 1125 = (-3 * n + n * n) 1125 = (-3n + n2) Solving 1125 = -3n + n2 Solving for variable 'n'. Reorder the terms: 1125 + 3n + -1n2 = -3n + 3n + n2 + -1n2 Combine like terms: -3n + 3n = 0 1125 + 3n + -1n2 = 0 + n2 + -1n2 1125 + 3n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 1125 + 3n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1125 + -3n + n2 = 0 Move the constant term to the right: Add '1125' to each side of the equation. -1125 + -3n + 1125 + n2 = 0 + 1125 Reorder the terms: -1125 + 1125 + -3n + n2 = 0 + 1125 Combine like terms: -1125 + 1125 = 0 0 + -3n + n2 = 0 + 1125 -3n + n2 = 0 + 1125 Combine like terms: 0 + 1125 = 1125 -3n + n2 = 1125 The n term is -3n. 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. -3n + 2.25 + n2 = 1125 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 1125 + 2.25 Combine like terms: 1125 + 2.25 = 1127.25 2.25 + -3n + n2 = 1127.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 1127.25 Calculate the square root of the right side: 33.574543928 Break this problem into two subproblems by setting (n + -1.5) equal to 33.574543928 and -33.574543928.Subproblem 1
n + -1.5 = 33.574543928 Simplifying n + -1.5 = 33.574543928 Reorder the terms: -1.5 + n = 33.574543928 Solving -1.5 + n = 33.574543928 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 33.574543928 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 33.574543928 + 1.5 n = 33.574543928 + 1.5 Combine like terms: 33.574543928 + 1.5 = 35.074543928 n = 35.074543928 Simplifying n = 35.074543928Subproblem 2
n + -1.5 = -33.574543928 Simplifying n + -1.5 = -33.574543928 Reorder the terms: -1.5 + n = -33.574543928 Solving -1.5 + n = -33.574543928 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -33.574543928 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -33.574543928 + 1.5 n = -33.574543928 + 1.5 Combine like terms: -33.574543928 + 1.5 = -32.074543928 n = -32.074543928 Simplifying n = -32.074543928Solution
The solution to the problem is based on the solutions from the subproblems. n = {35.074543928, -32.074543928}
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