Use the quadratic formula to solve the following quadratic equation: x^2−6x−20=20

Answer 1

To solve the quadratic equation x^2 - 6x - 20 = 20 using the quadratic formula, we first rearrange the equation to have the constant term on the right side:

x^2 - 6x - 20 - 20 = 0

Simplifying:

x^2 - 6x - 40 = 0

Now we can use the quadratic formula, which states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = 1, b = -6, and c = -40. Plugging these values into the quadratic formula:

x = (-(-6) ± √((-6)^2 - 4(1)(-40))) / (2(1))

Simplifying:

x = (6 ± √(36 + 160)) / 2

x = (6 ± √(196)) / 2

x = (6 ± 14) / 2

So, the solutions to the quadratic equation x^2 - 6x - 20 = 20 are:

x = (6 + 14) / 2 = 20 / 2 = 10

x = (6 - 14) / 2 = -8 / 2 = -4