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Simplifying n2 + -1n = 136 Reorder the terms: -1n + n2 = 136 Solving -1n + n2 = 136 Solving for variable 'n'. Reorder the terms: -136 + -1n + n2 = 136 + -136 Combine like terms: 136 + -136 = 0 -136 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '136' to each side of the equation. -136 + -1n + 136 + n2 = 0 + 136 Reorder the terms: -136 + 136 + -1n + n2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + -1n + n2 = 0 + 136 -1n + n2 = 0 + 136 Combine like terms: 0 + 136 = 136 -1n + n2 = 136 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 = 136 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 136 + 0.25 Combine like terms: 136 + 0.25 = 136.25 0.25 + -1n + n2 = 136.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 136.25 Calculate the square root of the right side: 11.67261753 Break this problem into two subproblems by setting (n + -0.5) equal to 11.67261753 and -11.67261753.Subproblem 1
n + -0.5 = 11.67261753 Simplifying n + -0.5 = 11.67261753 Reorder the terms: -0.5 + n = 11.67261753 Solving -0.5 + n = 11.67261753 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 = 11.67261753 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 11.67261753 + 0.5 n = 11.67261753 + 0.5 Combine like terms: 11.67261753 + 0.5 = 12.17261753 n = 12.17261753 Simplifying n = 12.17261753Subproblem 2
n + -0.5 = -11.67261753 Simplifying n + -0.5 = -11.67261753 Reorder the terms: -0.5 + n = -11.67261753 Solving -0.5 + n = -11.67261753 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 = -11.67261753 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -11.67261753 + 0.5 n = -11.67261753 + 0.5 Combine like terms: -11.67261753 + 0.5 = -11.17261753 n = -11.17261753 Simplifying n = -11.17261753Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.17261753, -11.17261753}
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