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Simplifying n2 + -3n = 90 Reorder the terms: -3n + n2 = 90 Solving -3n + n2 = 90 Solving for variable 'n'. Reorder the terms: -90 + -3n + n2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -3n + 90 + n2 = 0 + 90 Reorder the terms: -90 + 90 + -3n + n2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -3n + n2 = 0 + 90 -3n + n2 = 0 + 90 Combine like terms: 0 + 90 = 90 -3n + n2 = 90 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 90 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 90 + 2.25 Combine like terms: 90 + 2.25 = 92.25 2.25 + -3n + n2 = 92.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (n + -1.5) equal to 9.604686356 and -9.604686356.Subproblem 1
n + -1.5 = 9.604686356 Simplifying n + -1.5 = 9.604686356 Reorder the terms: -1.5 + n = 9.604686356 Solving -1.5 + n = 9.604686356 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 9.604686356 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 9.604686356 + 1.5 n = 9.604686356 + 1.5 Combine like terms: 9.604686356 + 1.5 = 11.104686356 n = 11.104686356 Simplifying n = 11.104686356Subproblem 2
n + -1.5 = -9.604686356 Simplifying n + -1.5 = -9.604686356 Reorder the terms: -1.5 + n = -9.604686356 Solving -1.5 + n = -9.604686356 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -9.604686356 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -9.604686356 + 1.5 n = -9.604686356 + 1.5 Combine like terms: -9.604686356 + 1.5 = -8.104686356 n = -8.104686356 Simplifying n = -8.104686356Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.104686356, -8.104686356}
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