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## Q. 1.6.4

Solving an Equation Containing a Radical (Square Root)

Solve  $x – \sqrt{15 – 2x }= 0.$

## Verified Solution

$x – \sqrt{15 – 2x }= 0$

Step 1         $x =\sqrt{15 – 2x}$               Isolate the radical.

Step 2         $x² = (\sqrt{15 – 2x })²$       Square each side.

x² = 15 – 2x                $(\sqrt{a })²= a$, for a ≥ 0.

Step 3        x² + 2x – 15 = 0               Write in standard form.

(x + 5)(x – 3) = 0                       Factor.

x + 5 = 0   or   x – 3 = 0            Zero-factor property

x = -5        or   x = 3                   Proposed solutions

Step 4
CHECK         $x – \sqrt{15 – 2x} = 0$        Original equation

$\left. \begin{matrix}-5 – \sqrt{15 – 2(-5)} ≟ 0&\text{Let} x = -5.\\ -5-\sqrt{25}≟ 0\\ -5-5≟ 0\\-10=0 & \text{False}\end{matrix}\right|\begin{matrix}3 – \sqrt{15 – 2(3)} ≟ 0&\text{Let} x = 3.\\ 3-\sqrt{9}≟ 0\\ 3-3≟ 0\\0=0 ✓& \text{ True}\end{matrix}$

As the check shows, only 3 is a solution, so the solution set is {3}.