Example 3
Completion requirements
| Example 3 |
Solve \(\sqrt {2x - 4} = 6\).
Step 1: Identify any restrictions on the variable.
\(\begin{align}
2x - 4 &\ge 0 \\
2x &\ge 4 \\
x &\ge 2, x \in \rm R \\
\end{align}\)
Step 2: Raise both sides of the equation to the exponent of two, and solve the equation.
\(\begin{align}
\sqrt {2x - 4} &= 6 \\
\left( {\sqrt {2x - 4} } \right)^2 &= 6^2 \\
2x - 4 &= 36 \\
2x &= 40 \\
x &= 20 \\
\end{align}\)
The solution is within the variable’s restrictions.
Step 3: Verify the solution.
The solution is \(x = 20\).
\(\begin{align}
2x - 4 &\ge 0 \\
2x &\ge 4 \\
x &\ge 2, x \in \rm R \\
\end{align}\)
Step 2: Raise both sides of the equation to the exponent of two, and solve the equation.
\(\begin{align}
\sqrt {2x - 4} &= 6 \\
\left( {\sqrt {2x - 4} } \right)^2 &= 6^2 \\
2x - 4 &= 36 \\
2x &= 40 \\
x &= 20 \\
\end{align}\)
The solution is within the variable’s restrictions.
Step 3: Verify the solution.
| Left Side | Right Side |
|---|---|
| \(\begin{array}{r} \sqrt {2x - 4} \\ \sqrt {2\left( {20} \right) - 4} \\ \sqrt {40 - 4} \\ \sqrt {36} \\ 6 \\ \end{array}\) | \(6\) |
| LS = RS \(\hspace{30pt}\) | |
The solution is \(x = 20\).