Deck 14: Quadratic Equations

Question 1

Solve for $x$ by factoring: $3 x(x-2)=x(2 x-3)$

Answer 1

$x=0,3$

Question 2

Solve for $x$ by factoring: $8 x^{2}=3 x$

Answer 2

$x=0,3 / 8$

Question 3

Solve for $x$ by factoring: $10 x(x+1)=4(4 x+1)$

Answer 3

$x=-0.4,1$

Question 4

Solve for $x$ by factoring: $3\left(x^{2}+4\right)+5 x=2 x^{2}+6(x+3)$

Question 5

Solve for $x$ by factoring: $x^{2}+5 x-84=0$

Question 6

Solve for $x$ by factoring: $2 x^{2}+12 x-80=0$

Question 7

Solve for $x$ by factoring: $x^{2}-4 x+4=0$

Question 8

Solve for $x$ by factoring: $x^{2}-7 x-30=0$

Question 9

Solve for $x$ by factoring: $x^{2}+14 x+45=0$

Question 10

Solve for $x$ by factoring: $x^{2}-11 x-60=0$

Question 11

Solve for $x$ by factoring: $2 x^{2}-5 x+2=0$

Question 12

Solve for $x$ by factoring: $3 x^{2}+x-4=0$

Question 13

Solve for $x$ by factoring: $\frac{x+2}{2}=\frac{10}{x+1}$

Question 14

Solve for $x$ by factoring: $\frac{2 x+1}{5}=\frac{4}{x-1}$

Question 15

Solve for $x$ by factoring: $4 x+\frac{6}{x}=25$

Question 16

Solve for $x$ by factoring: $7 x=\frac{28}{x+3}$

Question 17

Solve for $x$ by factoring: $5 x(x+3)+18=2 x(x-3)$

Question 18

Solve for $x$ by factoring: $2 x(x+1)-30=30$

Question 19

Solve for $x$ by factoring: $3 x(x-3)+22=2 x^{2}+4(x-5)$

Question 20

Solve for $x$ by factoring: $(x+3)^{2}=6 x+25$

Question 21

Solve for $x$ by factoring: $3(x+2)^{2}=-x$

Question 22

Solve for $x$ in terms of $a: 35 x^{2}-17 a x+2 a^{2}=0$

Question 23

Solve for $x$ in terms of $y: 2 x^{2}-3 x y-2 y^{2}=0$

Question 24

Solve for $x$ in terms of $a: x^{2}-a x-6 a^{2}=0$

Question 25

Solve for $x$ in terms of $y: 2 x^{2}+x y-y^{2}=0$

Question 26

Write a quadratic equation that has roots $x=-1$ and $x=4 / 3$ .

Question 27

Write a quadratic equation that has roots $x=\sqrt{6}$ and $x=\sqrt{3}$ .

Question 28

Write a quadratic equation that has roots $x=4$ and $x=-2$ .

Question 29

Solve this radical equation for $x$ and check: $\sqrt{x^{2}-3}=2 x+3$

Question 30

Solve this radical equation for $x$ and check: $\sqrt{x^{2}+9}-3=2$

Question 31

Solve this radical equation for $x$ and check: $\sqrt{2 x^{2}-1}+15=22$

Question 32

Solve this radical equation for $x$ and check: $\sqrt{x-3}=\frac{-10}{\sqrt{4-x}}$

Question 33

Solve and check this equation. Assume $p$ is nonzero: $3 p^{2}-2 p=7.42 p$

Question 34

Solve and check this equation. Assume $t$ is nonzero: at $-7.2 t^{2}=8 t$

Question 35

Solve for $x$ by completing the square: $x^{2}-3 x-9=0$

Question 36

Solve for $x$ by completing the square: $x^{2}-6 x-10=0$

Question 37

Solve for $x$ by completing the square: $x^{2}-8 x+15=0$

Question 38

Solve for $x$ by completing the square: $x^{2}+4 x-5=0$

Question 39

Solve for $x$ by completing the square: $9 x^{2}+12 x-22=0$

Question 40

Solve for $x$ by completing the square: $3 x^{2}+2 x-2=0$

Question 41

Solve for $x$ by completing the square: $2 x^{2}+5 x+2=0$

Question 42

Solve for $x$ by completing the square: $6 x^{2}-5 x-6=0$

Question 43

Solve for $x$ by completing the square: $3 x^{2}+5 x-2=0$

Question 44

Solve for $x$ by completing the square: $4 x^{2}+8 x+3=0$

Question 45

Solve for $x$ by completing the square: $2 x^{2}+x+1=0$

Question 46

Solve for $x$ by completing the square: $x^{2}+8 x+1=0$

Question 47

Use the quadratic formula to solve for $x$ to three significant digits: $x^{2}-8 x-10=0$

Question 48

Use the quadratic formula to solve for $x$ to three significant digits: $x^{2}-5 x-130=0$

Question 49

Use the quadratic formula to solve for $x$ to three significant digits: $9 x^{2}+81 x-18=0$

Question 50

Use the quadratic formula to solve for $x$ to three significant digits: $4 x^{2}-7 x+1=0$

Question 51

Use the quadratic formula to solve for $x$ to three significant digits: $3 x^{2}+33 x+4=0$

Question 52

Use the quadratic formula to solve for $x$ to three significant digits: $8 x^{2}+16 x+2=0$

Question 53

Use the quadratic formula to solve for $x$ to three significant digits: $4 x^{2}-8 x=1$

Question 54

Use the quadratic formula to solve for $x$ to three significant digits: $4 x^{2}+14 x-27=0$

Question 55

Use the quadratic formula to solve for $x$ to three significant digits: $x^{2}+6 x-9=0$

Question 56

Use the quadratic formula to solve for $x$ to three significant digits: $115 x^{2}-105 x+2=0$

Question 57

Use the quadratic formula to solve for $x$ to three significant digits: $2 x^{2}+3 x-5=0$

Question 58

Use the quadratic formula to solve for $x$ to three significant digits: $10 x^{2}-15 x+2=0$

Question 59

Use the quadratic formula to solve for $x$ to three significant digits: $x(3 x-4)=4(x+4)+1$

Question 60

Use the quadratic formula to solve for $x$ to three significant digits: $x\left(x^{2}+x+1\right)=x^{3}-28 x-1$

Question 61

Use the quadratic formula to solve for $x$ to three significant digits: $3(x+1)+(x-1)^{3}=(x+1)^{3}$

Question 62

Use the quadratic formula to solve for $x$ to three significant digits: $(8 x+3)^{2}=21 x(3 x+2)+8$

Question 63

Use the quadratic formula to solve for $x$ to three significant digits: $9 x^{2}+3 x+1=0$

Question 64

Use the quadratic formula to solve for $x$ to three significant digits: $9 x^{2}-24 x+20=0$

Question 65

Use the quadratic formula to solve for $x$ to three significant digits: $x^{2}-4 x+10=0$

Question 66

Use the quadratic formula to solve for $x$ to three significant digits: $3 x^{2}+4 x+2=0$

Question 67

Determine if the roots of $x^{2}-21 x-2=6$ are real or nonreal, and whether they are equal or unequal.

Question 68

Determine if the roots of $2 x^{2}+5 x+13=0$ are real or nonreal, and whether they are equal or unequal.

Question 69

Determine if the roots of $36 x^{2}+48 x+61=0$ are real or nonreal, and whether they are equal or unequal.

Question 70

Determine if the roots of $-18 x^{2}+65 x+61=0$ are real or nonreal, and whether they are equal or unequal.

Question 71

Determine if the roots of $8 x^{2}+2 x-12=0$ are real or nonreal, and whether they are equal or unequal.

Question 72

Determine if the roots of $3 x^{2}-6 x+3=0$ are real or nonreal, and whether they are equal or unequal.

Question 73

Find a number which added to its square equals 56.

Question 74

The square of a certain number less than the number itself, equals 67340 . What is the number?

Question 75

The difference of two numbers is seven and the product of their cubes is 512 . What are the numbers?

Question 76

The squares of two consecutive even numbers add to two more than eleven times their sum. What are the numbers?

Question 77

The difference of two numbers is 3 . The sum of their squares is 89 . What are the numbers?

Question 78

Find two numbers whose sum is 23 and the sum of whose squares is 277 .

Question 79

A rectangle is $3 \mathrm{~m}$ longer than twice its width and has an area of $324 \mathrm{~m}^{2}$ . What are its dimensions?

Question 80

A rectangle has a width that is 6 metres shorter than its length and an area of $27 \mathrm{~m}^{2}$ . Determine its dimensions.