To solve the equation [tex]\(8 + \sqrt{x+1} = 2\)[/tex], let's go through the steps systematically:
1. Isolate the square root term:
Begin by subtracting 8 from both sides of the equation to isolate the square root term.
[tex]\[
\sqrt{x+1} = 2 - 8
\][/tex]
2. Simplify the right-hand side:
Perform the subtraction on the right-hand side.
[tex]\[
\sqrt{x+1} = -6
\][/tex]
3. Analyze the result:
Now we have [tex]\(\sqrt{x+1} = -6\)[/tex]. Recall that the square root of a number represents a non-negative value — it cannot be negative.
Since the square root of any real number is always non-negative, it is impossible for [tex]\(\sqrt{x+1}\)[/tex] to equal [tex]\(-6\)[/tex]. Therefore, there is no value of [tex]\(x\)[/tex] that can satisfy this equation.
In conclusion:
[tex]\[
\text{There is no solution to the equation } 8 + \sqrt{x+1} = 2.
\][/tex]
