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Simplifying n2 + -3n + -147 = 0 Reorder the terms: -147 + -3n + n2 = 0 Solving -147 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '147' to each side of the equation. -147 + -3n + 147 + n2 = 0 + 147 Reorder the terms: -147 + 147 + -3n + n2 = 0 + 147 Combine like terms: -147 + 147 = 0 0 + -3n + n2 = 0 + 147 -3n + n2 = 0 + 147 Combine like terms: 0 + 147 = 147 -3n + n2 = 147 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 = 147 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 147 + 2.25 Combine like terms: 147 + 2.25 = 149.25 2.25 + -3n + n2 = 149.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 149.25 Calculate the square root of the right side: 12.216791723 Break this problem into two subproblems by setting (n + -1.5) equal to 12.216791723 and -12.216791723.Subproblem 1
n + -1.5 = 12.216791723 Simplifying n + -1.5 = 12.216791723 Reorder the terms: -1.5 + n = 12.216791723 Solving -1.5 + n = 12.216791723 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 = 12.216791723 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 12.216791723 + 1.5 n = 12.216791723 + 1.5 Combine like terms: 12.216791723 + 1.5 = 13.716791723 n = 13.716791723 Simplifying n = 13.716791723Subproblem 2
n + -1.5 = -12.216791723 Simplifying n + -1.5 = -12.216791723 Reorder the terms: -1.5 + n = -12.216791723 Solving -1.5 + n = -12.216791723 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 = -12.216791723 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -12.216791723 + 1.5 n = -12.216791723 + 1.5 Combine like terms: -12.216791723 + 1.5 = -10.716791723 n = -10.716791723 Simplifying n = -10.716791723Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.716791723, -10.716791723}
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