Question : Solve the equation by the square root property. If possible : 2158618

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express imaginary solutions in the form a + bi.

1) 4x² = 60

A) {30}

B) {16}

C) {±15}

D) {±√(15)}

2) 3x² = 75

A) {0}

B) {±5√(3)}

C) {±3}

D) {±5}

3) 81x² = 361

A) {± (19/81)}

B) {(19/81)}

C) {± (19/9)}

D) {(19/9)}

4) 25x² + 4 = 0

A) {± (2/5)}

B) {± (2/25)}

C) {± (2/25)i}

D) {± (2/5)i}

5) 13x² - 2 = 0

A) {± (√(13)/2)}

B) {± (√(13)/26)}

C) {± (√(2)/13)}

D) {± (√(26)/13)}

6) (x - 4)² = 25

A) {29}

B) {5, -5}

C) {9, -1}

D) {-1, -9}

7) (x + 2)² = 17

A) {± (√(17)/2)}

B) {±√(17)}

C) {2 ± √(17)}

D) {-2 ± √(17)}

8) (x + 9)² = 28

A) {-9 ± 2√(14)}

B) {±2√(7)}

C) {2√(7) ± 9}

D) {-9 ± 2√(7)}

9) (x - (1/2))² = (9/4)

A) {-4, 2}

B) {-2, 1}

C) {-1, 2}

D) {-2, 4}

10) (x + (5/4))² = (7/16)

A) {(-5 ± √(7)/4)}

B) {-3, (1/2)}

C) {(5 ± √(7)/4)}

D) {(√(7) ± 5/4)}

11) (x - 5)² = -16

A) {5 ± 4i}

B) {± (4i/5)}

C) {4 ± 5i}

D) {-5 ± 4i}

12) x² - 20x + 100 = 36

A) {-16, -4}

B) {4, 16}

C) {-26, 46}

D) {16}

Solve the problem.

13) If f(x) = (x - 3)² , find all values of x for which f(x) = 4.

A) 2, -2

B) -5, 1

C) 7

D) 1, 5

14) If g(x) = (x + 5)², find all values of x for which g(x) = 10.

A) 5 ± √(10)

B) -5 ± √(10)

C) ±√(10)

D) ± (√(10)/5)

15) If h(x) = (x - (3/2))², find all values of x for which h(x) = (9/4).

A) 0, 6

B) 0, 3

C) -6, 0

D) -3, 0

16) If f(x) = (x - 7)², find all values of x for which f(x) = -4.

A) 7i ± 2

B) 7 ± 2i

C) ± (2i/7)

D) -7 ± 2i

Complete the square for the binomial. Then factor the resulting perfect square trinomial.

17) x² + 8x

A) 8; x² + 8x + 8 = (x + 64)²

B) 4; x² + 8x + 4 = (x + 16)²

C) 16; x² + 8x + 16 = (x + 4)²

D) 64; x² + 8x + 64 = (x + 8)²

18) x² - 10x

A) 100; x² - 10x + 100 = (x - 10)²

B) 25; x² - 10x + 25 = (x - 5)²

C) 100; x² - 10x - 100 = (x - 10)²

D) 25; x² - 10x - 25 = (x - 5)²

19) x² + (1/6)x

A) 144; x² + (1/6)x + 144 = (x +12)²

B) (1/36); x² + (1/6)x + (1/36) = (x + (1/6))²

C) (1/144); x² + (1/6)x + (1/144) = (x + (1/12))²

D) (1/12); x² + (1/6)x + (1/12) = (x + (1/6))²

20) x² - (2/3)x

A) (1/9); x² - (2/3)x + (1/9) = (x - (1/3))²

B) (4/9); x² - (2/3)x + (4/9) = (x - (2/3))²

C) (1/9); x² - (2/3)x + (1/9) = (x + (1/3))²

D) (2/9); x² - (2/3)x + (2/9) = (x - (1/3))²

21) x² + 7x

A) 14; x² + 7x + 14 = (x + 7)²

B) (49/4); x² + 7x + (49/4) = (x + (7/2))²

C) (49/4); x² + 7x - (49/4) = (x - (7/2))²

D) (49/2); x² + 7x + (49/2) = (x + (49/2))²

22) x² - 9x

A) (9/2); x² - 9x + (9/2) = (x - (9/2))²

B) (81/4); x² - 9x + (81/4) = (x - (9/2))²

C) 81; x² - 9x + 81 = (x - 9)²

D) (81/4); x² - 9x - (81/4) = (x - (9/2))²

23) x² + (4/7)x

A) (2/49); x² + (4/7)x + (2/49) = (x + (2/7))²

B) (4/49); x² + (4/7)x + (4/49) = (x + (2/7))²

C) (8/49); x² + (4/7)x + (8/49) = (x + (4/7))²

D) (4/7); x² + (4/7)x + (4/7) = (x + (2/7))²