Question

homework 10: section 2.6
score: 20/180 answered: 2/18
question 2
solve the equation: \\(\sqrt{m + 19} = 3\\)
answer: \\(m = \\)
question help: message instructor

Explanation:

Step1: Square both sides to eliminate the square root

To solve the equation \(\sqrt{m + 19}=3\), we square both sides of the equation. Squaring the left side \((\sqrt{m + 19})^2\) gives \(m + 19\), and squaring the right side \(3^2\) gives \(9\). So we get the equation:
\(m + 19=9\)

Step2: Solve for m

To isolate \(m\), we subtract 19 from both sides of the equation \(m + 19=9\). Subtracting 19 from the left side gives \(m\), and subtracting 19 from the right side gives \(9-19\). Calculating \(9 - 19\) we get \(- 10\). So:
\(m=9 - 19=-10\)
We should also check the solution by substituting \(m = - 10\) back into the original equation. Substituting into \(\sqrt{m + 19}\), we have \(\sqrt{-10 + 19}=\sqrt{9} = 3\), which matches the right side of the original equation. So \(m=-10\) is a valid solution.

Answer:

\(m=-10\)