What are the solutions to the equation 2n^2=-10n-5 ?

The solutions to the equation 2n^2=-10n-5 are n=(-5+sqrt(15))/2 ,n=-(5+sqrt(15))/2

Find the zeros of 2n^2=-10n-5

The zeros of 2n^2=-10n-5 are n=(-5+sqrt(15))/2 ,n=-(5+sqrt(15))/2

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2 n^{2} = - 10 n - 5

n = \frac{- 5 + 15}{2}, n = - \frac{5 + 15}{2}

Decimal Notation

n = - 0.56350 \dots, n = - 4.43649 \dots

Solution steps

2 n^{2} = - 10 n - 5

Move

5

to the left side

2 n^{2} + 5 = - 10 n

Move

10 n

to the left side

2 n^{2} + 5 + 10 n = 0

Write in the standard form

a x^{2} + b x + c = 0

2 n^{2} + 10 n + 5 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- 10 \pm 1 0 ^{2} - 4 \cdot 2 \cdot 5}{2 \cdot 2}

1 0^{2} - 4 \cdot 2 \cdot 5 = 215

n_{1, 2} = \frac{- 10 \pm 2 15}{2 \cdot 2}

Separate the solutions

n_{1} = \frac{- 10 + 2 15}{2 \cdot 2}, n_{2} = \frac{- 10 - 2 15}{2 \cdot 2}

n = \frac{- 10 + 2 15}{2 \cdot 2} : \frac{- 5 + 15}{2}

n = \frac{- 10 - 2 15}{2 \cdot 2} : - \frac{5 + 15}{2}

The solutions to the quadratic equation are:

n = \frac{- 5 + 15}{2}, n = - \frac{5 + 15}{2}

n^{2} + 3 n - 12 = 6

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

0 = - x^{2} - 4 x + 4

4 x^{2} + 5 x = 2 x^{2} + 3 x

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

What are the solutions to the equation 2n^2=-10n-5 ?
The solutions to the equation 2n^2=-10n-5 are n=(-5+sqrt(15))/2 ,n=-(5+sqrt(15))/2
Find the zeros of 2n^2=-10n-5
The zeros of 2n^2=-10n-5 are n=(-5+sqrt(15))/2 ,n=-(5+sqrt(15))/2