What are the solutions of 2x² + 16x + 34 = 0?

Solution:

The given equation is:

2x² + 16x + 34 = 0

2(x² + 8x + 17)

The roots of the equation of x² + 8x + 17 are calculated from the formula

\(\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

Since \({b^{2}-4ac}\) is negative the roots are complex conjugate

=\(\frac{-8\pm \sqrt{8^{2}-4(1)(17)}}{2(1)}\)

=\(\frac{-8\pm \sqrt{64-68}}{2}\)

=\(\frac{-8\pm \sqrt{-4}}{2}\)

=\(\frac{-8\pm 2\sqrt{-1}}{2}\)

=\(\frac{-8\pm 2i}{2}\)

The roots are -4 + i and -4 - i.

What are the solutions of 2x² + 16x + 34 = 0?

Summary:

The solutions of 2x² + 16x + 34 = 0 are x = -4 + i and -4 - i.