What are the solutions to the equation (n+7)^2=-2n ?

The solutions to the equation (n+7)^2=-2n are n=-8+sqrt(15),n=-8-sqrt(15)

Find the zeros of (n+7)^2=-2n

The zeros of (n+7)^2=-2n are n=-8+sqrt(15),n=-8-sqrt(15)

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(n + 7)^{2} = - 2 n

n = - 8 + 15, n = - 8 - 15

Decimal Notation

n = - 4.12701 \dots, n = - 11.87298 \dots

Solution steps

(n + 7)^{2} = - 2 n

Expand

(n + 7)^{2} : n^{2} + 14 n + 49

n^{2} + 14 n + 49 = - 2 n

Move

2 n

to the left side

n^{2} + 16 n + 49 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- 16 \pm 1 6 ^{2} - 4 \cdot 1 \cdot 49}{2 \cdot 1}

1 6^{2} - 4 \cdot 1 \cdot 49 = 215

n_{1, 2} = \frac{- 16 \pm 2 15}{2 \cdot 1}

Separate the solutions

n_{1} = \frac{- 16 + 2 15}{2 \cdot 1}, n_{2} = \frac{- 16 - 2 15}{2 \cdot 1}

n = \frac{- 16 + 2 15}{2 \cdot 1} : - 8 + 15

n = \frac{- 16 - 2 15}{2 \cdot 1} : - 8 - 15

The solutions to the quadratic equation are:

n = - 8 + 15, n = - 8 - 15

a - (10 - a) = 30

∣ x - 1 ∣ \geq 4

- 7 - 263

x^{2} - 10 x - 6 = 0

- 9 - 2

What are the solutions to the equation (n+7)^2=-2n ?
The solutions to the equation (n+7)^2=-2n are n=-8+sqrt(15),n=-8-sqrt(15)
Find the zeros of (n+7)^2=-2n
The zeros of (n+7)^2=-2n are n=-8+sqrt(15),n=-8-sqrt(15)