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Simplifying n2 + -9n + -99 = 0 Reorder the terms: -99 + -9n + n2 = 0 Solving -99 + -9n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -9n + 99 + n2 = 0 + 99 Reorder the terms: -99 + 99 + -9n + n2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -9n + n2 = 0 + 99 -9n + n2 = 0 + 99 Combine like terms: 0 + 99 = 99 -9n + n2 = 99 The n term is -9n. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9n + 20.25 + n2 = 99 + 20.25 Reorder the terms: 20.25 + -9n + n2 = 99 + 20.25 Combine like terms: 99 + 20.25 = 119.25 20.25 + -9n + n2 = 119.25 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = 119.25 Calculate the square root of the right side: 10.920164834 Break this problem into two subproblems by setting (n + -4.5) equal to 10.920164834 and -10.920164834.Subproblem 1
n + -4.5 = 10.920164834 Simplifying n + -4.5 = 10.920164834 Reorder the terms: -4.5 + n = 10.920164834 Solving -4.5 + n = 10.920164834 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 10.920164834 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 10.920164834 + 4.5 n = 10.920164834 + 4.5 Combine like terms: 10.920164834 + 4.5 = 15.420164834 n = 15.420164834 Simplifying n = 15.420164834Subproblem 2
n + -4.5 = -10.920164834 Simplifying n + -4.5 = -10.920164834 Reorder the terms: -4.5 + n = -10.920164834 Solving -4.5 + n = -10.920164834 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -10.920164834 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -10.920164834 + 4.5 n = -10.920164834 + 4.5 Combine like terms: -10.920164834 + 4.5 = -6.420164834 n = -6.420164834 Simplifying n = -6.420164834Solution
The solution to the problem is based on the solutions from the subproblems. n = {15.420164834, -6.420164834}
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