8x^2 - 22x - 408 = 0.

Answer 1

To solve this quadratic equation, we can either factor it or use the quadratic formula.

Let's try factoring it first:

8x^2 - 22x - 408 = 0

Let's find two numbers whose product is -408 and whose sum is -22. The numbers we're looking for are -34 and 12.

8x^2 - 22x - 408 = (8x + 12)(x - 34) = 0

Now we can set each factor equal to zero:

8x + 12 = 0 or x - 34 = 0

Solving for x in each equation:

8x = -12 or x = 34

x = -12/8 or x = 34

Simplifying:

x = -3/2 or x = 34

Therefore, the solutions to the equation 8x^2 - 22x - 408 = 0 are x = -3/2 and x = 34.