Question

Solve for the roots in simplest form using the quadratic formula: x^2 + 61 =-10x

Answer 1

9514 1404 393

Answer:

  -5 ± 6i

Step-by-step explanation:

To use the quadratic formula, we need the equation in standard form. Adding 10x gives ...

  x^2 +10x +61 = 0

Then a=1, b=10, c=61, and the solutions are ...

  $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-10\pm\sqrt{10^2-4(1)(61)}}{2(1)}\\\\=\dfrac{-10\pm\sqrt{-144}}{2}=\dfrac{-10\pm12i}{2}\\\\ \boxed{x=\{-5-6i,-6+6i\}}$