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Simplifying n2 + 10n + -3 = 0 Reorder the terms: -3 + 10n + n2 = 0 Solving -3 + 10n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 10n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + 10n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 10n + n2 = 0 + 3 10n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 10n + n2 = 3 The n term is 10n. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10n + 25 + n2 = 3 + 25 Reorder the terms: 25 + 10n + n2 = 3 + 25 Combine like terms: 3 + 25 = 28 25 + 10n + n2 = 28 Factor a perfect square on the left side: (n + 5)(n + 5) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (n + 5) equal to 5.291502622 and -5.291502622.Subproblem 1
n + 5 = 5.291502622 Simplifying n + 5 = 5.291502622 Reorder the terms: 5 + n = 5.291502622 Solving 5 + n = 5.291502622 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + n = 5.291502622 + -5 n = 5.291502622 + -5 Combine like terms: 5.291502622 + -5 = 0.291502622 n = 0.291502622 Simplifying n = 0.291502622Subproblem 2
n + 5 = -5.291502622 Simplifying n + 5 = -5.291502622 Reorder the terms: 5 + n = -5.291502622 Solving 5 + n = -5.291502622 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = -5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + n = -5.291502622 + -5 n = -5.291502622 + -5 Combine like terms: -5.291502622 + -5 = -10.291502622 n = -10.291502622 Simplifying n = -10.291502622Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.291502622, -10.291502622}
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