Let's carefully review Adrian's steps and identify any mistakes.
1. Given Equation:
[tex]\( x^2 + 9 = 16 \)[/tex]
2. Review of Adrian's Line 2:
Adrian wrote:
[tex]\( x + 3 = \pm 4 \)[/tex]
Here, Adrian made an error. To solve [tex]\( x^2 + 9 = 16 \)[/tex], he should have first isolated [tex]\( x^2 \)[/tex] by subtracting 9 from both sides of the equation.
3. Correct Step 2:
Subtract 9 from both sides:
[tex]\[
x^2 + 9 - 9 = 16 - 9
\][/tex]
Simplifying the equation:
[tex]\[
x^2 = 7
\][/tex]
4. Correct Step 3:
Next, take the square root of both sides:
[tex]\[
x = \pm \sqrt{7}
\][/tex]
Given these corrected steps, the correct solutions for the equation [tex]\( x^2 + 9 = 16 \)[/tex] are [tex]\( x = \sqrt{7} \)[/tex] and [tex]\( x = -\sqrt{7} \)[/tex].
Identifying Adrian's Mistake:
Adrian made a mistake in Line 2. In Line 2, he should have subtracted 9 from both sides of the equation because it is not part of the expression that is squared.
Correct Statement:
"In Line 2, he should have subtracted 9 from both sides of the equation because it is not part of the expression that is squared."
