solving the equation (x+4)(x-4)=9 Eric stated that the solution would be x+4=9>x=5 or (x-4)=9=>x=13
However one of these solution fails to work when subsituted back to the original equation. Why?olve and explain the reasoning. Can someone please help me?
To solve the equation (x+4)(x-4) = 9, we can start by expanding the equation:
(x+4)(x-4) = 9
x^2 - 16 = 9
x^2 = 9 + 16
x^2 = 25
Next, we can take the square root of both sides to solve for x:
x = ±√25
x = ±5
Now let's substitute each solution back into the original equation to see if it holds true.
For x = 5:
(x+4)(x-4) = 9
(5+4)(5-4) = 9
9 * 1 = 9
9 = 9
The equation holds true.
For x = -5:
(x+4)(x-4) = 9
(-5+4)(-5-4) = 9
-1 * -9 = 9
9 = 9
The equation holds true.
So both x = 5 and x = -5 are valid solutions.
Now let's understand why Eric's claims of x = 5 and x = 13 are incorrect:
For x = 13:
(x+4)(x-4) = 9
(13+4)(13-4) = 9
17 * 9 = 9
153 = 9
As we see, 153 does not equal 9. So, x = 13 is an incorrect solution.
To summarize, the correct solutions to the equation (x+4)(x-4) = 9 are x = 5 and x = -5. The claim of x = 13 is incorrect as it does not satisfy the equation when substituted back.