Solve n^(2)=(n-1)⋅(n-1 n-2)

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

n_{1} = - 1 - 3, n_{2} = - 1 + 3

Alternative Form

n_{1} \approx - 2.732051, n_{2} \approx 0.732051

Evaluate

n^{2} = (n - 1) (n - 1 \times n - 2)

Simplify

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n^{2} = - 2 (n - 1)

Expand the expression

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n^{2} = - 2 n + 2

Move the expression to the left side

n^{2} + 2 n - 2 = 0

Substitute a= 1,b= 2 and c= - 2 into the quadratic formula n = \frac{- b \pm b ^{2} - 4 a c}{2 a}

n = \frac{- 2 \pm 2 ^{2} - 4 ( - 2 )}{2}

Simplify the expression

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n = \frac{- 2 \pm 12}{2}

Simplify the radical expression

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n = \frac{- 2 \pm 2 3}{2}

Separate the equation into 2 possible cases

n = \frac{- 2 + 2 3}{2} n = \frac{- 2 - 2 3}{2}

Simplify the expression

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n = - 1 + 3 n = \frac{- 2 - 2 3}{2}

Simplify the expression

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n = - 1 + 3 n = - 1 - 3

Solution

n_{1} = - 1 - 3, n_{2} = - 1 + 3

Alternative Form

n_{1} \approx - 2.732051, n_{2} \approx 0.732051

Show Solution