Page 153 - Math Course 2 (Book 1)

Radical Equations

Radical Equation with an
Expression Your Turn!

Variable in Radical
Example FREE-FALL HEIGHT

An object is dropped from an unknown height and
Solve x – 3 + 8 = 15 reaches the ground in 7 seconds.
h
x – 3 + 8 = 15 Original equation Use the equation t = 4 to f nd from what height
it is dropped.

x – 3 = 7 Subtract 8 from each side. A. 28 ft
B. 11 ft
2
( x – 3 ) = (7) 2 Square each side. C. 49 ft
D. 784 ft
2
x – 3 = 49 ( x – 3 ) = x – 3
Answer
x = 52 Add 3 to each side.

Radical Equation with an Expression
Answer The solution is 52.
Solve x + 4 + 6 = 14
Variable on Each Side A. 64
B. 60
C. 4
Example D. 196

Answer
Solve 2 – y = y

2 – y = y Original equation

2
( 2 – y ) = y 2 Square each side.
2 – y = y 2 Simplify.

2
0 = y y – 2 Subtract 2 and add y to Variable on Each Side
each side.
Solve y = 2y + 3
0 = (y + 2)(y – 1) Factor. A. 3

B. –1
y + 2 = 0 or y – 1 = 0 Zero Product Property. C. 0
D. –3
y = –2 y = 1 Solve.
Check
Answer
2 – y = y 2 – y = y
2 – (–2) = (–2) 2 – (–1) = (1)

4 = (–2) 1 = (1)
2 = –2 1 = 1

Since –2 does not satisfy the
Answer original equation, 1 is the only
solution.

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