Question

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

Answer 1

Answer:

2($x^{2}$+8x+17)

Step-by-step explanation:

Factor out 2 of the equation.

Answer 2

Answer:

For real numbers: no solution

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

Step-by-step 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.

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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

$x = \dfrac{-8 \pm \sqrt{8^2 - 4(1)(17)}}{2(1)}$

$x = \dfrac{-8 \pm \sqrt{64 - 68}}{2}$

$x = \dfrac{-8 \pm \sqrt{-64}}{2}$

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.

$x = \dfrac{-8 \pm 8i}{2}$

$x = -4 \pm 4i$