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Simplifying n2 + -5n = 28 Reorder the terms: -5n + n2 = 28 Solving -5n + n2 = 28 Solving for variable 'n'. Reorder the terms: -28 + -5n + n2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -5n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -5n + 28 + n2 = 0 + 28 Reorder the terms: -28 + 28 + -5n + n2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -5n + n2 = 0 + 28 -5n + n2 = 0 + 28 Combine like terms: 0 + 28 = 28 -5n + n2 = 28 The n term is -5n. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5n + 6.25 + n2 = 28 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 28 + 6.25 Combine like terms: 28 + 6.25 = 34.25 6.25 + -5n + n2 = 34.25 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (n + -2.5) equal to 5.852349955 and -5.852349955.Subproblem 1
n + -2.5 = 5.852349955 Simplifying n + -2.5 = 5.852349955 Reorder the terms: -2.5 + n = 5.852349955 Solving -2.5 + n = 5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = 5.852349955 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 5.852349955 + 2.5 n = 5.852349955 + 2.5 Combine like terms: 5.852349955 + 2.5 = 8.352349955 n = 8.352349955 Simplifying n = 8.352349955Subproblem 2
n + -2.5 = -5.852349955 Simplifying n + -2.5 = -5.852349955 Reorder the terms: -2.5 + n = -5.852349955 Solving -2.5 + n = -5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = -5.852349955 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -5.852349955 + 2.5 n = -5.852349955 + 2.5 Combine like terms: -5.852349955 + 2.5 = -3.352349955 n = -3.352349955 Simplifying n = -3.352349955Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.352349955, -3.352349955}
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