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Simplifying -3n2 + -14n + 13 = -4n2 + 5 Reorder the terms: 13 + -14n + -3n2 = -4n2 + 5 Reorder the terms: 13 + -14n + -3n2 = 5 + -4n2 Solving 13 + -14n + -3n2 = 5 + -4n2 Solving for variable 'n'. Reorder the terms: 13 + -5 + -14n + -3n2 + 4n2 = 5 + -4n2 + -5 + 4n2 Combine like terms: 13 + -5 = 8 8 + -14n + -3n2 + 4n2 = 5 + -4n2 + -5 + 4n2 Combine like terms: -3n2 + 4n2 = 1n2 8 + -14n + 1n2 = 5 + -4n2 + -5 + 4n2 Reorder the terms: 8 + -14n + 1n2 = 5 + -5 + -4n2 + 4n2 Combine like terms: 5 + -5 = 0 8 + -14n + 1n2 = 0 + -4n2 + 4n2 8 + -14n + 1n2 = -4n2 + 4n2 Combine like terms: -4n2 + 4n2 = 0 8 + -14n + 1n2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -14n + -8 + n2 = 0 + -8 Reorder the terms: 8 + -8 + -14n + n2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -14n + n2 = 0 + -8 -14n + n2 = 0 + -8 Combine like terms: 0 + -8 = -8 -14n + n2 = -8 The n term is -14n. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14n + 49 + n2 = -8 + 49 Reorder the terms: 49 + -14n + n2 = -8 + 49 Combine like terms: -8 + 49 = 41 49 + -14n + n2 = 41 Factor a perfect square on the left side: (n + -7)(n + -7) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (n + -7) equal to 6.403124237 and -6.403124237.Subproblem 1
n + -7 = 6.403124237 Simplifying n + -7 = 6.403124237 Reorder the terms: -7 + n = 6.403124237 Solving -7 + n = 6.403124237 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = 6.403124237 + 7 Combine like terms: -7 + 7 = 0 0 + n = 6.403124237 + 7 n = 6.403124237 + 7 Combine like terms: 6.403124237 + 7 = 13.403124237 n = 13.403124237 Simplifying n = 13.403124237Subproblem 2
n + -7 = -6.403124237 Simplifying n + -7 = -6.403124237 Reorder the terms: -7 + n = -6.403124237 Solving -7 + n = -6.403124237 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = -6.403124237 + 7 Combine like terms: -7 + 7 = 0 0 + n = -6.403124237 + 7 n = -6.403124237 + 7 Combine like terms: -6.403124237 + 7 = 0.596875763 n = 0.596875763 Simplifying n = 0.596875763Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.403124237, 0.596875763}
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