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Simplifying 325 = n(125 + -1n) + 50n 325 = (125 * n + -1n * n) + 50n 325 = (125n + -1n2) + 50n Reorder the terms: 325 = 125n + 50n + -1n2 Combine like terms: 125n + 50n = 175n 325 = 175n + -1n2 Solving 325 = 175n + -1n2 Solving for variable 'n'. Reorder the terms: 325 + -175n + n2 = 175n + -175n + -1n2 + n2 Combine like terms: 175n + -175n = 0 325 + -175n + n2 = 0 + -1n2 + n2 325 + -175n + n2 = -1n2 + n2 Combine like terms: -1n2 + n2 = 0 325 + -175n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-325' to each side of the equation. 325 + -175n + -325 + n2 = 0 + -325 Reorder the terms: 325 + -325 + -175n + n2 = 0 + -325 Combine like terms: 325 + -325 = 0 0 + -175n + n2 = 0 + -325 -175n + n2 = 0 + -325 Combine like terms: 0 + -325 = -325 -175n + n2 = -325 The n term is -175n. Take half its coefficient (-87.5). Square it (7656.25) and add it to both sides. Add '7656.25' to each side of the equation. -175n + 7656.25 + n2 = -325 + 7656.25 Reorder the terms: 7656.25 + -175n + n2 = -325 + 7656.25 Combine like terms: -325 + 7656.25 = 7331.25 7656.25 + -175n + n2 = 7331.25 Factor a perfect square on the left side: (n + -87.5)(n + -87.5) = 7331.25 Calculate the square root of the right side: 85.622718948 Break this problem into two subproblems by setting (n + -87.5) equal to 85.622718948 and -85.622718948.Subproblem 1
n + -87.5 = 85.622718948 Simplifying n + -87.5 = 85.622718948 Reorder the terms: -87.5 + n = 85.622718948 Solving -87.5 + n = 85.622718948 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '87.5' to each side of the equation. -87.5 + 87.5 + n = 85.622718948 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + n = 85.622718948 + 87.5 n = 85.622718948 + 87.5 Combine like terms: 85.622718948 + 87.5 = 173.122718948 n = 173.122718948 Simplifying n = 173.122718948Subproblem 2
n + -87.5 = -85.622718948 Simplifying n + -87.5 = -85.622718948 Reorder the terms: -87.5 + n = -85.622718948 Solving -87.5 + n = -85.622718948 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '87.5' to each side of the equation. -87.5 + 87.5 + n = -85.622718948 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + n = -85.622718948 + 87.5 n = -85.622718948 + 87.5 Combine like terms: -85.622718948 + 87.5 = 1.877281052 n = 1.877281052 Simplifying n = 1.877281052Solution
The solution to the problem is based on the solutions from the subproblems. n = {173.122718948, 1.877281052}
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