Solve for x: √(x-6) + 20 = 21
Understand the Problem
The question asks to solve for x in the equation √(x-6) + 20 = 21. This involves isolating and then squaring the square root term to find the value of x.
Answer
$x = 7$
Answer for screen readers
$x = 7$
Steps to Solve
-
Isolate the square root Subtract 20 from both sides of the equation to isolate the square root term: $$ \sqrt{x-6} + 20 - 20 = 21 - 20 $$ $$ \sqrt{x-6} = 1 $$
-
Square both sides Square both sides of the equation to eliminate the square root: $$ (\sqrt{x-6})^2 = 1^2 $$ $$ x-6 = 1 $$
-
Solve for x Add 6 to both sides of the equation to solve for $x$: $$ x - 6 + 6 = 1 + 6 $$ $$ x = 7 $$
$x = 7$
More Information
We can check our answer by substituting $x = 7$ back into the original equation: $$ \sqrt{7-6} + 20 = \sqrt{1} + 20 = 1 + 20 = 21 $$ This confirms that $x = 7$ is the correct solution.
Tips
A common mistake is forgetting to isolate the square root before squaring both sides. If you square the original equation without isolating the square root, you will have a harder time solving the problem to get to the correct answer.
AI-generated content may contain errors. Please verify critical information
