Lesson 10-3

Example 1 Variable in Radical
CLIFF DIVING  Two divers dive simultaneously off of 2 cliffs. The first diver reaches the water in 2 seconds and the second diver reaches the water 2 seconds later. What heights did the divers dive from?
1st diver																	2nd diver	
t = /4	Original equation						t = /4								Original equation
2 = /4	Replace t with 2.						4 = /4							Replace t with 4.
8 = 	Multiply each side by 4.		16 = 								Multiply each side by 4.
82 = ()2	Square each side.						162 = ()2						Square each side.
64 = h		Simplify.											256 = h									Simplify.
Check by substituting 64 and 256 for h in the original equation.

Example 2 Radical Equation with an Expression
Solve  = 7.
= 7	Original Equation
() = 7	Square each side.
2x – 3 = 49	() = 2x – 3
2x = 52		Add 3 to each side.
x = 26		Divide each side by 2. Check this result.
	
Example 3 Variable on Each Side
Solve  – 3 = x.
 – 3 = x	Original equation
 = x + 3	Add 3 to each side.
() = (x + 3)	Square each side.
x + 5 = x + 6x + 9	Simplify.
0 = x + 5x + 4		Subtract x and 5 from each side.
0 = (x + 1)(x + 4)		Factor.
x + 1 = 0    or    x + 4 = 0	Zero Product Property
x = -1	x = -4		Solve.

CHECK:	
	 – 3 = x	 – 3 = x
	 – 3 =? -1	 – 3  -4
	 – 3 =? -1	 – 3  -4
	2 – 3 =? -1	1 – 3  -4
	-1 = -1	-2 -4
Since -4 does not satisfy the original equation, -1 is the only solution.