Question

Solve for the roots in simplest form by completing the square 6x^2+120x+2070=0

Answer 1

Answer:

Step-by-step explanation:

First, we can divide out the common factor, 6

$6x^2 + 120x + 2070 = 0\\x^2 + 20x + 345 = 0$

Now we complete the square

$(x^2 + 20x + (\frac{20}{2})^2) + 345 - (\frac{20}{2})^2\\(x^2 + 20x + 100) + 345 - 100\\(x+10)^2 + 245$

$(x+10)^2 = -245\\x + 10 = \sqrt{-245}\\x = i\sqrt{245} - 10\\x = -10 \pm i\sqrt{245}$