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Simplifying n2 + -9n + -144 = 0 Reorder the terms: -144 + -9n + n2 = 0 Solving -144 + -9n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -9n + 144 + n2 = 0 + 144 Reorder the terms: -144 + 144 + -9n + n2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -9n + n2 = 0 + 144 -9n + n2 = 0 + 144 Combine like terms: 0 + 144 = 144 -9n + n2 = 144 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 = 144 + 20.25 Reorder the terms: 20.25 + -9n + n2 = 144 + 20.25 Combine like terms: 144 + 20.25 = 164.25 20.25 + -9n + n2 = 164.25 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = 164.25 Calculate the square root of the right side: 12.816005618 Break this problem into two subproblems by setting (n + -4.5) equal to 12.816005618 and -12.816005618.Subproblem 1
n + -4.5 = 12.816005618 Simplifying n + -4.5 = 12.816005618 Reorder the terms: -4.5 + n = 12.816005618 Solving -4.5 + n = 12.816005618 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 = 12.816005618 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 12.816005618 + 4.5 n = 12.816005618 + 4.5 Combine like terms: 12.816005618 + 4.5 = 17.316005618 n = 17.316005618 Simplifying n = 17.316005618Subproblem 2
n + -4.5 = -12.816005618 Simplifying n + -4.5 = -12.816005618 Reorder the terms: -4.5 + n = -12.816005618 Solving -4.5 + n = -12.816005618 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 = -12.816005618 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -12.816005618 + 4.5 n = -12.816005618 + 4.5 Combine like terms: -12.816005618 + 4.5 = -8.316005618 n = -8.316005618 Simplifying n = -8.316005618Solution
The solution to the problem is based on the solutions from the subproblems. n = {17.316005618, -8.316005618}
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