Answer:
2([tex]x^{2}[/tex]+8x+17)
Step-by-step explanation:
Factor out 2 of the equation.
Answer:
For real numbers: no solution
For complex numbers: [tex] x = -4 \pm 4i [/tex]
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.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
We have a = 1; b = 8; c = 17
[tex] x = \dfrac{-8 \pm \sqrt{8^2 - 4(1)(17)}}{2(1)} [/tex]
[tex] x = \dfrac{-8 \pm \sqrt{64 - 68}}{2} [/tex]
[tex] x = \dfrac{-8 \pm \sqrt{-64}}{2} [/tex]
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.
[tex] x = \dfrac{-8 \pm 8i}{2} [/tex]
[tex] x = -4 \pm 4i [/tex]
