Solving equations

Section 1.4

Solving equations with radicals

Solve the equation

32 x

22)3(2 x

92 x

7 x

7xCheck for extraneous solutions

Check for extraneous solutions.

32 x

X=-7 is an extraneous solution.

There are no solutions

372

39

33

Solve

xx 12

212 xx

120 2 xx

340 xx

04 x 03 x

3x4x

Check for extraneous solutions!

Solve for x and check for extraneous solutions.

181 xx

22 )1()81( xx

1281 2 xxx

xx 100 2 )10(0 xx

10,0 xx

X=0 is our solution x=-10 is an extraneous solution

Two Radicals

If there are two radicals in the equation, make sure you have one on each side of the equal sign before squaring both sides

4162 xx

1462 xx

Solve for x and check for extraneous solutions.

4162 xx

224162 xx

414162 xxx

444162 xxxx

421 xx

22 421 xx

)4(4122 xxx

164122 xxx

01522 xx

035 xx

X=5

X = -3 is an extraneous solution

Factor the equation with fractional exponents to solve for x

0183 3

1

3

2

xx

036 3

1

3

1

xx

03,06 3

1

3

1

xx

3,6 3

1

3

1

xx

3

3

3

13

3

3

1

3,6

xx

27,216 xx

Factor the equation with negative exponents to solve for x

0103 12 xx

025 11 xx

02,05 11 xx

2,5 11 xx

21

,51

xx

2

1,

5

1

xx

Factor by grouping

(2x+3)² + 4(2x+3) + 5 = 0

(2x+3)² + 4(2x+3) = -5

(2x+3)(2x+3+4) = -5

(2x+3)(2x+7) = -5

2x + 3 = -5 2x + 7 = -5

2x = -8 2x = -12

x=-4 x=-6