Answer:
x = 5, -5, 3, -3
Explanation:
First, substitute u = x^2 into the equation, and we have
u^2 - 34u + 225 = 0
u = x^2
Factor u^2 −34u +225 using the AC method, and we get
( u - 25) ( u - 9) = 0
We know If any individual factor on the left side of the equation is equal to
0, the entire expression will be equal to 0, so
u - 25 = 0
u - 9 = 0
Next, we set u - 25 equal to 0 and solve for u, and we get
u = 25
Then set u - 9 equal to 0 and solve for u, and we get
u = 9
The final solution is all the values that make (u−25)(u−9) = 0 true.
u =25,9
Substitute the real value of u=x^2 back into the solved equation.
x^2 = 25
(x^2)^1 = 9
x^2 = 25
x = 5, -5
Now we solve the second equation
(x^2)^1 = 9
x = 3, -3
So, the answers are: 5, -5, 3, -3