Solve Equations with Square Roots: example 9.81

Solve: $3 \sqrt{3 x - 5} - 8 = 4$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve: $2 \sqrt{4 a + 2} - 16 = 16$ .

How did it go?

	$3 \sqrt{3 x - 5} - 8 = 4$
Isolate the radical.	$3 \sqrt{3 x - 5} = 12$
Square both sides of the equation.	${(3 \sqrt{3 x - 5})}^{2} = {(12)}^{2}$
Simplify, then solve the new equation.	$9 (3 x - 5) = 144$
Distribute.	$27 x - 45 = 144$
Solve the equation.	$27 x = 189$
	$x = 7$
Check the answer.
	The solution is $x = 7$ .

	$3 \sqrt{3 x - 5} - 8 = 4$
Isolate the radical.	$3 \sqrt{3 x - 5} = 12$
Square both sides of the equation.	${(3 \sqrt{3 x - 5})}^{2} = {(12)}^{2}$
Simplify, then solve the new equation.	$9 (3 x - 5) = 144$
Distribute.	$27 x - 45 = 144$
Solve the equation.	$27 x = 189$
	$x = 7$
Check the answer.
	The solution is $x = 7$ .