What are the solutions to the equation 5x^2+x=-1 ?

The solutions to the equation 5x^2+x=-1 are x=-1/10+i(sqrt(19))/(10),x=-1/10-i(sqrt(19))/(10)

Find the zeros of 5x^2+x=-1

The zeros of 5x^2+x=-1 are x=-1/10+i(sqrt(19))/(10),x=-1/10-i(sqrt(19))/(10)

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5 x^{2} + x = - 1

x = - \frac{1}{10} + i \frac{19}{10}, x = - \frac{1}{10} - i \frac{19}{10}

Solution steps

5 x^{2} + x = - 1

Move

1

to the left side

5 x^{2} + x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 5 \cdot 1}{2 \cdot 5}

Simplify

1^{2} - 4 \cdot 5 \cdot 1 : 19 i

x_{1, 2} = \frac{- 1 \pm 19 i}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- 1 + 19 i}{2 \cdot 5}, x_{2} = \frac{- 1 - 19 i}{2 \cdot 5}

x = \frac{- 1 + 19 i}{2 \cdot 5} : - \frac{1}{10} + i \frac{19}{10}

x = \frac{- 1 - 19 i}{2 \cdot 5} : - \frac{1}{10} - i \frac{19}{10}

The solutions to the quadratic equation are:

x = - \frac{1}{10} + i \frac{19}{10}, x = - \frac{1}{10} - i \frac{19}{10}

2 x^{2} + 24 = - 264

x^{2} - 3 x - 10 = 0

15 + 4 x^{2} = - 2 x + 3 x^{2} + 4

(x + 4) (x - 1) = 0

m^{2} - 6 m + 10 = 0

What are the solutions to the equation 5x^2+x=-1 ?
The solutions to the equation 5x^2+x=-1 are x=-1/10+i(sqrt(19))/(10),x=-1/10-i(sqrt(19))/(10)
Find the zeros of 5x^2+x=-1
The zeros of 5x^2+x=-1 are x=-1/10+i(sqrt(19))/(10),x=-1/10-i(sqrt(19))/(10)