Subscribe $4.99/month

Un-lock Verified Step-by-Step Experts Answers.

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

Our Website is free to use.
To help us grow, you can support our team with a Small Tip.

All the data tables that you may search for.

Need Help? We got you covered.

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

Products

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

Need Help? We got you covered.

Chapter 1

Q. 1.6.4

Solving an Equation Containing a Radical (Square Root)

Solve  x – \sqrt{15 – 2x }= 0.

Step-by-Step

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}.