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 = 11.87298 \dots, n = 4.12701 \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 ( - 16 ) ^{2} - 4 \cdot 1 \cdot 49}{2 \cdot 1}

(- 16)^{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

x^{2} + 2 x - 5 = 0

6 x^{2} - 8 x - 30 = 0

- 7 x + x^{2} = - 3 x^{2} + 6

\frac{1}{4} x^{2} + 3 x = x - 4

- x^{2} + 8 x + 1 = 0

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)