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Simplifying n2 + -30n + -28 = 0 Reorder the terms: -28 + -30n + n2 = 0 Solving -28 + -30n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -30n + 28 + n2 = 0 + 28 Reorder the terms: -28 + 28 + -30n + n2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -30n + n2 = 0 + 28 -30n + n2 = 0 + 28 Combine like terms: 0 + 28 = 28 -30n + n2 = 28 The n term is -30n. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30n + 225 + n2 = 28 + 225 Reorder the terms: 225 + -30n + n2 = 28 + 225 Combine like terms: 28 + 225 = 253 225 + -30n + n2 = 253 Factor a perfect square on the left side: (n + -15)(n + -15) = 253 Calculate the square root of the right side: 15.905973721 Break this problem into two subproblems by setting (n + -15) equal to 15.905973721 and -15.905973721.Subproblem 1
n + -15 = 15.905973721 Simplifying n + -15 = 15.905973721 Reorder the terms: -15 + n = 15.905973721 Solving -15 + n = 15.905973721 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + n = 15.905973721 + 15 Combine like terms: -15 + 15 = 0 0 + n = 15.905973721 + 15 n = 15.905973721 + 15 Combine like terms: 15.905973721 + 15 = 30.905973721 n = 30.905973721 Simplifying n = 30.905973721Subproblem 2
n + -15 = -15.905973721 Simplifying n + -15 = -15.905973721 Reorder the terms: -15 + n = -15.905973721 Solving -15 + n = -15.905973721 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + n = -15.905973721 + 15 Combine like terms: -15 + 15 = 0 0 + n = -15.905973721 + 15 n = -15.905973721 + 15 Combine like terms: -15.905973721 + 15 = -0.905973721 n = -0.905973721 Simplifying n = -0.905973721Solution
The solution to the problem is based on the solutions from the subproblems. n = {30.905973721, -0.905973721}
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