What are the solutions to the equation (n+5)^2=-2n ?

The solutions to the equation (n+5)^2=-2n are n=-6+sqrt(11),n=-6-sqrt(11)

Find the zeros of (n+5)^2=-2n

The zeros of (n+5)^2=-2n are n=-6+sqrt(11),n=-6-sqrt(11)

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(n + 5)^{2} = - 2 n

n = - 6 + 11, n = - 6 - 11

Decimal Notation

n = - 2.68337 \dots, n = - 9.31662 \dots

Solution steps

(n + 5)^{2} = - 2 n

Expand

(n + 5)^{2} : n^{2} + 10 n + 25

n^{2} + 10 n + 25 = - 2 n

Move

2 n

to the left side

n^{2} + 12 n + 25 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 1 \cdot 25}{2 \cdot 1}

1 2^{2} - 4 \cdot 1 \cdot 25 = 211

n_{1, 2} = \frac{- 12 \pm 2 11}{2 \cdot 1}

Separate the solutions

n_{1} = \frac{- 12 + 2 11}{2 \cdot 1}, n_{2} = \frac{- 12 - 2 11}{2 \cdot 1}

n = \frac{- 12 + 2 11}{2 \cdot 1} : - 6 + 11

n = \frac{- 12 - 2 11}{2 \cdot 1} : - 6 - 11

The solutions to the quadratic equation are:

n = - 6 + 11, n = - 6 - 11

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What are the solutions to the equation (n+5)^2=-2n ?
The solutions to the equation (n+5)^2=-2n are n=-6+sqrt(11),n=-6-sqrt(11)
Find the zeros of (n+5)^2=-2n
The zeros of (n+5)^2=-2n are n=-6+sqrt(11),n=-6-sqrt(11)