Question
use the quadratic formula to solve the following quadratic equation: x^2 - 6x - 20 = 20
Answers
GPT 3.5
To solve the quadratic equation x^2 - 6x - 20 = 20, we first need to rewrite the equation in the form ax^2 + bx + c = 0.
Rearranging terms, we have:
x^2 - 6x - 40 = 0
Now, we can identify the values of a, b, and c for the quadratic formula:
a = 1
b = -6
c = -40
Plugging these values into the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a), we get:
x = (-(-6) ± √((-6)^2 - 4(1)(-40))) / (2(1))
Simplifying further:
x = (6 ± √(36 + 160)) / 2
x = (6 ± √196) / 2
Now, we can find the two solutions by evaluating both the positive and negative square roots of 196:
x = (6 + 14) / 2 or x = (6 - 14) / 2
Simplifying:
x = 20 / 2 or x = -8 / 2
x = 10 or x = -4
Therefore, the solutions to the quadratic equation x^2 - 6x - 20 = 20 are x = 10 and x = -4.
Rearranging terms, we have:
x^2 - 6x - 40 = 0
Now, we can identify the values of a, b, and c for the quadratic formula:
a = 1
b = -6
c = -40
Plugging these values into the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a), we get:
x = (-(-6) ± √((-6)^2 - 4(1)(-40))) / (2(1))
Simplifying further:
x = (6 ± √(36 + 160)) / 2
x = (6 ± √196) / 2
Now, we can find the two solutions by evaluating both the positive and negative square roots of 196:
x = (6 + 14) / 2 or x = (6 - 14) / 2
Simplifying:
x = 20 / 2 or x = -8 / 2
x = 10 or x = -4
Therefore, the solutions to the quadratic equation x^2 - 6x - 20 = 20 are x = 10 and x = -4.