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Simplifying n2 + -1n = 48 Reorder the terms: -1n + n2 = 48 Solving -1n + n2 = 48 Solving for variable 'n'. Reorder the terms: -48 + -1n + n2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -1n + 48 + n2 = 0 + 48 Reorder the terms: -48 + 48 + -1n + n2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -1n + n2 = 0 + 48 -1n + n2 = 0 + 48 Combine like terms: 0 + 48 = 48 -1n + n2 = 48 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 48 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 48 + 0.25 Combine like terms: 48 + 0.25 = 48.25 0.25 + -1n + n2 = 48.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (n + -0.5) equal to 6.946221995 and -6.946221995.Subproblem 1
n + -0.5 = 6.946221995 Simplifying n + -0.5 = 6.946221995 Reorder the terms: -0.5 + n = 6.946221995 Solving -0.5 + n = 6.946221995 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 6.946221995 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 6.946221995 + 0.5 n = 6.946221995 + 0.5 Combine like terms: 6.946221995 + 0.5 = 7.446221995 n = 7.446221995 Simplifying n = 7.446221995Subproblem 2
n + -0.5 = -6.946221995 Simplifying n + -0.5 = -6.946221995 Reorder the terms: -0.5 + n = -6.946221995 Solving -0.5 + n = -6.946221995 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -6.946221995 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -6.946221995 + 0.5 n = -6.946221995 + 0.5 Combine like terms: -6.946221995 + 0.5 = -6.446221995 n = -6.446221995 Simplifying n = -6.446221995Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.446221995, -6.446221995}
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