To solve this equation, let's make a substitution to simplify the expression. Let's substitute u = x^2 - 9.
So, the equation becomes: u^2 - 8u + 7 = 0.
Now, we can factor this quadratic equation:
(u - 7)(u - 1) = 0
Setting each factor equal to zero gives us:
u - 7 = 0 or u - 1 = 0u = 7 or u = 1
Now, substitute back x^2 - 9 for u:
x^2 - 9 = 7 or x^2 - 9 = 1
x^2 = 16 or x^2 = 10
Taking the square root of both sides gives us two possible solutions for x:
x = ±4 or x = ±√10
Therefore, the solutions to the given equation are:x = 4x = -4x = √10x = -√10
To solve this equation, let's make a substitution to simplify the expression. Let's substitute u = x^2 - 9.
So, the equation becomes: u^2 - 8u + 7 = 0.
Now, we can factor this quadratic equation:
(u - 7)(u - 1) = 0
Setting each factor equal to zero gives us:
u - 7 = 0 or u - 1 = 0
u = 7 or u = 1
Now, substitute back x^2 - 9 for u:
x^2 - 9 = 7 or x^2 - 9 = 1
x^2 = 16 or x^2 = 10
Taking the square root of both sides gives us two possible solutions for x:
x = ±4 or x = ±√10
Therefore, the solutions to the given equation are:
x = 4
x = -4
x = √10
x = -√10