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Simplifying 0.5n2 + -2n + -16 = 42 Reorder the terms: -16 + -2n + 0.5n2 = 42 Solving -16 + -2n + 0.5n2 = 42 Solving for variable 'n'. Reorder the terms: -16 + -42 + -2n + 0.5n2 = 42 + -42 Combine like terms: -16 + -42 = -58 -58 + -2n + 0.5n2 = 42 + -42 Combine like terms: 42 + -42 = 0 -58 + -2n + 0.5n2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -116 + -4n + n2 = 0 Move the constant term to the right: Add '116' to each side of the equation. -116 + -4n + 116 + n2 = 0 + 116 Reorder the terms: -116 + 116 + -4n + n2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + -4n + n2 = 0 + 116 -4n + n2 = 0 + 116 Combine like terms: 0 + 116 = 116 -4n + n2 = 116 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 116 + 4 Reorder the terms: 4 + -4n + n2 = 116 + 4 Combine like terms: 116 + 4 = 120 4 + -4n + n2 = 120 Factor a perfect square on the left side: (n + -2)(n + -2) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (n + -2) equal to 10.95445115 and -10.95445115.Subproblem 1
n + -2 = 10.95445115 Simplifying n + -2 = 10.95445115 Reorder the terms: -2 + n = 10.95445115 Solving -2 + n = 10.95445115 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 10.95445115 + 2 Combine like terms: -2 + 2 = 0 0 + n = 10.95445115 + 2 n = 10.95445115 + 2 Combine like terms: 10.95445115 + 2 = 12.95445115 n = 12.95445115 Simplifying n = 12.95445115Subproblem 2
n + -2 = -10.95445115 Simplifying n + -2 = -10.95445115 Reorder the terms: -2 + n = -10.95445115 Solving -2 + n = -10.95445115 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -10.95445115 + 2 Combine like terms: -2 + 2 = 0 0 + n = -10.95445115 + 2 n = -10.95445115 + 2 Combine like terms: -10.95445115 + 2 = -8.95445115 n = -8.95445115 Simplifying n = -8.95445115Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.95445115, -8.95445115}
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