Question

Solve 2x^2+16x+34=0?????

Answer 1

For real numbers: no solution

For complex numbers:
`x = -4 \pm 4i`

Explanation:

2x^2 + 16x + 34 = 0

Divide both sides by 2.

x^2 + 8x + 17 = 0

There are no two numbers whose product is 17 and whose sum is 8, so this polynomial is not factorable.

We can use the quadratic formula.

`x = (-b \pm √(b^2 - 4ac))/(2a)`

We have a = 1; b = 8; c = 17

`x = (-8 \pm √(8^2 - 4(1)(17)))/(2(1))`

`x = (-8 \pm √(64 - 68))/(2)`

`x = (-8 \pm √(-64))/(2)`

If you have not learned imaginary or complex numbers, stop here. Since the discriminant is negative, there is no real solution.

If you have learned complex numbers, then we continue.

`x = (-8 \pm 8i)/(2)`

`x = -4 \pm 4i`

Answer 2

2(
`x^(2)`+8x+17)

Explanation:

Factor out 2 of the equation.