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Simplifying n2 + 10n + -53 = 0 Reorder the terms: -53 + 10n + n2 = 0 Solving -53 + 10n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + 10n + 53 + n2 = 0 + 53 Reorder the terms: -53 + 53 + 10n + n2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 10n + n2 = 0 + 53 10n + n2 = 0 + 53 Combine like terms: 0 + 53 = 53 10n + n2 = 53 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 = 53 + 25 Reorder the terms: 25 + 10n + n2 = 53 + 25 Combine like terms: 53 + 25 = 78 25 + 10n + n2 = 78 Factor a perfect square on the left side: (n + 5)(n + 5) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (n + 5) equal to 8.831760866 and -8.831760866.Subproblem 1
n + 5 = 8.831760866 Simplifying n + 5 = 8.831760866 Reorder the terms: 5 + n = 8.831760866 Solving 5 + n = 8.831760866 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 = 8.831760866 + -5 Combine like terms: 5 + -5 = 0 0 + n = 8.831760866 + -5 n = 8.831760866 + -5 Combine like terms: 8.831760866 + -5 = 3.831760866 n = 3.831760866 Simplifying n = 3.831760866Subproblem 2
n + 5 = -8.831760866 Simplifying n + 5 = -8.831760866 Reorder the terms: 5 + n = -8.831760866 Solving 5 + n = -8.831760866 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 = -8.831760866 + -5 Combine like terms: 5 + -5 = 0 0 + n = -8.831760866 + -5 n = -8.831760866 + -5 Combine like terms: -8.831760866 + -5 = -13.831760866 n = -13.831760866 Simplifying n = -13.831760866Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.831760866, -13.831760866}
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