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Simplifying n2 + -1n + -148 = 0 Reorder the terms: -148 + -1n + n2 = 0 Solving -148 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '148' to each side of the equation. -148 + -1n + 148 + n2 = 0 + 148 Reorder the terms: -148 + 148 + -1n + n2 = 0 + 148 Combine like terms: -148 + 148 = 0 0 + -1n + n2 = 0 + 148 -1n + n2 = 0 + 148 Combine like terms: 0 + 148 = 148 -1n + n2 = 148 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 = 148 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 148 + 0.25 Combine like terms: 148 + 0.25 = 148.25 0.25 + -1n + n2 = 148.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 148.25 Calculate the square root of the right side: 12.175795662 Break this problem into two subproblems by setting (n + -0.5) equal to 12.175795662 and -12.175795662.Subproblem 1
n + -0.5 = 12.175795662 Simplifying n + -0.5 = 12.175795662 Reorder the terms: -0.5 + n = 12.175795662 Solving -0.5 + n = 12.175795662 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 = 12.175795662 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 12.175795662 + 0.5 n = 12.175795662 + 0.5 Combine like terms: 12.175795662 + 0.5 = 12.675795662 n = 12.675795662 Simplifying n = 12.675795662Subproblem 2
n + -0.5 = -12.175795662 Simplifying n + -0.5 = -12.175795662 Reorder the terms: -0.5 + n = -12.175795662 Solving -0.5 + n = -12.175795662 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 = -12.175795662 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -12.175795662 + 0.5 n = -12.175795662 + 0.5 Combine like terms: -12.175795662 + 0.5 = -11.675795662 n = -11.675795662 Simplifying n = -11.675795662Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.675795662, -11.675795662}
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