1001 Algebra Problems.PDF

636. c.First, put the equation into standard form
     by expanding the expression on the left side,
     and then moving all terms to the left side of
     the equation:

(3x– 8)^2 = 45

9 x^2 – 48x+ 64 = 45

9 x^2 – 48x+ 19 = 0

Now, apply the quadratic formula with a= 9,

b= –48, and c= 19 to obtain:

x= = =

= =

637. d.We first multiply both sides of the equation
     by 100, then divide both sides by 20 in order
     to make the coefficients integers; this will help
     with the simplification process. Doing so
     yields the equivalent equation x^2 – 11x+ 10 =


638. Now, apply the quadratic formula with a= 1,
     b= –11, and c= 10 to obtain:

x= = =

= = 1, 10

638. d.Apply the quadratic formula with a= 1,
     b= –3, and c= –3 to obtain:

x= = =

639. b.The simplification process will be easier if
     we first eliminate the fractions by multiplying
     both sides of the equation  61 x^2 – ^53 x+ 1 = 0 by 6.
     Doing so yields the equivalent equation x^2 – 10x

+ 6 = 0. Now, apply the quadratic formula

with a= 1,b= –10, and c= 6 to obtain:

x= = =

= = 5 ± 19 

640. b.First, put the equation into standard form
     by expanding the expression on the left side,
     and then moving all terms to the left side of
     the equation:

(x– 3)(2x+ 1) =x(x– 4)

2 x^2 – 6x+x– 3 =x^2 – 4x

x^2 – x– 3 = 0

Now, apply the quadratic formula with a= 1,

b= –1, and c= –3 to obtain:

x= = =

Set 41 (Page 97)

641. a.Isolate the squared expression on one side,
     take the square root of both sides, and solve
     forx, as follows:

4 x^2 = 3

x^2 = ^34 

x= ± ^34 = ±^34 = ± 2 ^3

1 ±^13 

2

–(–1) ±(–1)^2 – 4(1)(–3)

2(1)

–b±b^2 –4ac

2 a

10 ± 2^19 

2

10 ±^76 

2

–(–10) ±(–10)^2 –4(1)(6)

2(1)

–b±b^2 –4ac

2 a

3±^21 

2

–(–3) ±(–3)^2 – 4(1)(3)

2(1)

–b±b^2 –4ac

2 a

11 ±9

2

11 ±^81 

2

–(–11) ±(–11)^2 – 4(1)(–10)

2(1)

–b±b^2 –4ac

2 a

–8 ±3^5 

3

–48 ±18^5 

18

–48 ±^1620 

18

–(–48) ±(–48)^2 –4(9)(19)

2(9)

–b±b^2 –4ac

2 a

ANSWERS & EXPLANATIONS–