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Simplifying n2 + -46n = 88 Reorder the terms: -46n + n2 = 88 Solving -46n + n2 = 88 Solving for variable 'n'. Reorder the terms: -88 + -46n + n2 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + -46n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + -46n + 88 + n2 = 0 + 88 Reorder the terms: -88 + 88 + -46n + n2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -46n + n2 = 0 + 88 -46n + n2 = 0 + 88 Combine like terms: 0 + 88 = 88 -46n + n2 = 88 The n term is -46n. Take half its coefficient (-23). Square it (529) and add it to both sides. Add '529' to each side of the equation. -46n + 529 + n2 = 88 + 529 Reorder the terms: 529 + -46n + n2 = 88 + 529 Combine like terms: 88 + 529 = 617 529 + -46n + n2 = 617 Factor a perfect square on the left side: (n + -23)(n + -23) = 617 Calculate the square root of the right side: 24.839484697 Break this problem into two subproblems by setting (n + -23) equal to 24.839484697 and -24.839484697.Subproblem 1
n + -23 = 24.839484697 Simplifying n + -23 = 24.839484697 Reorder the terms: -23 + n = 24.839484697 Solving -23 + n = 24.839484697 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + n = 24.839484697 + 23 Combine like terms: -23 + 23 = 0 0 + n = 24.839484697 + 23 n = 24.839484697 + 23 Combine like terms: 24.839484697 + 23 = 47.839484697 n = 47.839484697 Simplifying n = 47.839484697Subproblem 2
n + -23 = -24.839484697 Simplifying n + -23 = -24.839484697 Reorder the terms: -23 + n = -24.839484697 Solving -23 + n = -24.839484697 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + n = -24.839484697 + 23 Combine like terms: -23 + 23 = 0 0 + n = -24.839484697 + 23 n = -24.839484697 + 23 Combine like terms: -24.839484697 + 23 = -1.839484697 n = -1.839484697 Simplifying n = -1.839484697Solution
The solution to the problem is based on the solutions from the subproblems. n = {47.839484697, -1.839484697}
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