Let's solve this equation step by step.
First, expand the left side of the equation:
(x-5)(x+5) = x^2 + 5x - 5x - 25(x-5)(x+5) = x^2 - 25
Now simplify the right side of the equation:
(x-3)^2 + 2 = (x-3)(x-3) + 2(x-3)^2 + 2 = x^2 - 3x - 3x + 9 + 2(x-3)^2 + 2 = x^2 - 6x + 11
Now we can set the expanded left side equal to the simplified right side:
x^2 - 25 = x^2 - 6x + 11
Subtract x^2 from both sides to get:
-25 = -6x + 11
Subtract 11 from both sides to get:
-36 = -6x
Divide by -6 to get the solution for x:
x = 6
Therefore, the solution to the equation is x = 6.
Let's solve this equation step by step.
First, expand the left side of the equation:
(x-5)(x+5) = x^2 + 5x - 5x - 25
(x-5)(x+5) = x^2 - 25
Now simplify the right side of the equation:
(x-3)^2 + 2 = (x-3)(x-3) + 2
(x-3)^2 + 2 = x^2 - 3x - 3x + 9 + 2
(x-3)^2 + 2 = x^2 - 6x + 11
Now we can set the expanded left side equal to the simplified right side:
x^2 - 25 = x^2 - 6x + 11
Subtract x^2 from both sides to get:
-25 = -6x + 11
Subtract 11 from both sides to get:
-36 = -6x
Divide by -6 to get the solution for x:
x = 6
Therefore, the solution to the equation is x = 6.