To solve the equation
[tex]\[
\sqrt{x + 3} + 9 = 7
\][/tex]
we will isolate the square root term and analyze the situation step-by-step.
1. Isolate the Square Root Term:
Start by subtracting 9 from both sides of the equation:
[tex]\[
\sqrt{x + 3} = 7 - 9
\][/tex]
2. Simplify the Right Side:
Simplify the right side of the equation:
[tex]\[
\sqrt{x + 3} = -2
\][/tex]
3. Analyze the Result:
Recall that the square root of a number represents a non-negative value, that is:
[tex]\[
\sqrt{x + 3} \geq 0
\][/tex]
Therefore, it is impossible for the square root of any number to be negative. Thus, the equation
[tex]\[
\sqrt{x + 3} = -2
\][/tex]
cannot have any real solutions.
Hence, the given equation
[tex]\[
\sqrt{x + 3} + 9 = 7
\][/tex]
has no solution.
Given this logical analysis, we conclude that the equation has:
[tex]\[
\text{No solution}
\][/tex]
