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Simplifying n2 + 3n + -988 = 0 Reorder the terms: -988 + 3n + n2 = 0 Solving -988 + 3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '988' to each side of the equation. -988 + 3n + 988 + n2 = 0 + 988 Reorder the terms: -988 + 988 + 3n + n2 = 0 + 988 Combine like terms: -988 + 988 = 0 0 + 3n + n2 = 0 + 988 3n + n2 = 0 + 988 Combine like terms: 0 + 988 = 988 3n + n2 = 988 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 = 988 + 2.25 Reorder the terms: 2.25 + 3n + n2 = 988 + 2.25 Combine like terms: 988 + 2.25 = 990.25 2.25 + 3n + n2 = 990.25 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = 990.25 Calculate the square root of the right side: 31.468237955 Break this problem into two subproblems by setting (n + 1.5) equal to 31.468237955 and -31.468237955.Subproblem 1
n + 1.5 = 31.468237955 Simplifying n + 1.5 = 31.468237955 Reorder the terms: 1.5 + n = 31.468237955 Solving 1.5 + n = 31.468237955 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 = 31.468237955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = 31.468237955 + -1.5 n = 31.468237955 + -1.5 Combine like terms: 31.468237955 + -1.5 = 29.968237955 n = 29.968237955 Simplifying n = 29.968237955Subproblem 2
n + 1.5 = -31.468237955 Simplifying n + 1.5 = -31.468237955 Reorder the terms: 1.5 + n = -31.468237955 Solving 1.5 + n = -31.468237955 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 = -31.468237955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = -31.468237955 + -1.5 n = -31.468237955 + -1.5 Combine like terms: -31.468237955 + -1.5 = -32.968237955 n = -32.968237955 Simplifying n = -32.968237955Solution
The solution to the problem is based on the solutions from the subproblems. n = {29.968237955, -32.968237955}
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