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Simplifying n2 + 5n + -153 = 0 Reorder the terms: -153 + 5n + n2 = 0 Solving -153 + 5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '153' to each side of the equation. -153 + 5n + 153 + n2 = 0 + 153 Reorder the terms: -153 + 153 + 5n + n2 = 0 + 153 Combine like terms: -153 + 153 = 0 0 + 5n + n2 = 0 + 153 5n + n2 = 0 + 153 Combine like terms: 0 + 153 = 153 5n + n2 = 153 The n term is 5n. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5n + 6.25 + n2 = 153 + 6.25 Reorder the terms: 6.25 + 5n + n2 = 153 + 6.25 Combine like terms: 153 + 6.25 = 159.25 6.25 + 5n + n2 = 159.25 Factor a perfect square on the left side: (n + 2.5)(n + 2.5) = 159.25 Calculate the square root of the right side: 12.619429464 Break this problem into two subproblems by setting (n + 2.5) equal to 12.619429464 and -12.619429464.Subproblem 1
n + 2.5 = 12.619429464 Simplifying n + 2.5 = 12.619429464 Reorder the terms: 2.5 + n = 12.619429464 Solving 2.5 + n = 12.619429464 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = 12.619429464 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 12.619429464 + -2.5 n = 12.619429464 + -2.5 Combine like terms: 12.619429464 + -2.5 = 10.119429464 n = 10.119429464 Simplifying n = 10.119429464Subproblem 2
n + 2.5 = -12.619429464 Simplifying n + 2.5 = -12.619429464 Reorder the terms: 2.5 + n = -12.619429464 Solving 2.5 + n = -12.619429464 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = -12.619429464 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -12.619429464 + -2.5 n = -12.619429464 + -2.5 Combine like terms: -12.619429464 + -2.5 = -15.119429464 n = -15.119429464 Simplifying n = -15.119429464Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.119429464, -15.119429464}
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