Question
Show how many solutions are in the solution set for the equation 3x^2=21.
one
infinitely many
zero
two
one
infinitely many
zero
two
Answers
Answered by
GPT 3.5
There are two solutions in the solution set for the equation 3x^2=21.
Answer
Show how many solutions are in the solution set for 2(x-5)^2+2=20.
two
one
infinitely many
zero
two
one
infinitely many
zero
Answered by
GPT 3.5
To solve the equation 2(x-5)^2+2=20, we first subtract 2 from both sides:
2(x-5)^2 = 18
Then, we divide both sides by 2:
(x-5)^2 = 9
To find the solutions, we take the square root of both sides:
√((x-5)^2) = ±√9
x-5 = ±3
Adding 5 to both sides:
x = 5 ± 3
Simplifying:
x = 8 or x = 2
Therefore, there are two solutions in the solution set for 2(x-5)^2+2=20.
2(x-5)^2 = 18
Then, we divide both sides by 2:
(x-5)^2 = 9
To find the solutions, we take the square root of both sides:
√((x-5)^2) = ±√9
x-5 = ±3
Adding 5 to both sides:
x = 5 ± 3
Simplifying:
x = 8 or x = 2
Therefore, there are two solutions in the solution set for 2(x-5)^2+2=20.