Solving Quadratic Equations

solve by factoring

100

The solution to 

(x + 4)(x + 1) = 0

x = -4, -1

200

The solution to

x^2 - x = 0

x = 0 and x = 1

300

The solution to 

x^2 - x -12 = 0

x = 4, -3

400

The solution to 

x^2 +3x = 40

x = 5, -8

500

The solution to 

18x^2 -3x = 15

x = 1, - 5/6

solve by square root method

100

The solution to 

x^2 = 16

x = +- 4

200

The solution to 

3x^2 = 27

x = +-3

300

The solution to 

3x^2 = 21

 

x =+-sqrt 7

400

The solution to 

14n^2 +1 = 1513

x=+-6sqrt3

500

The solution to 

6x^2+10=-134

x=+-2isqrt6

solve by quadratic formula

100

The solution to 

x^2 - 4x + 1 = 0

x = 2 +-sqrt 3

200

The solution to 

x^2 - 7x = 18

x = 9, -2

300

The solution to 

x^2 + 9x - 11 = 0

 

x = (-9 +- 5sqrt5)/2

400

The solution to 

x^2 - 3x + 7 = 0

 

x = (3 +- isqrt19)/2

500

The solution to 

-3x^2 + 4x - 4 = 0

 

x = (2 +-2isqrt2)/3

discriminant & number/type of the root(s)

100

The discriminant, number & type of root for

x²+12x+32=0

d=16

2 real, rational roots

200

The discriminant, number & type of root for

x^2 -4x +1 = 0

d=12

2 real, irrational roots

300

The discriminant, number & type of root for 

3x^2 +5x = 2

d=49

2 real, rational roots

400

The discriminant, number & type of root for

4x^2 + 7 = 9x

d= -31

2 imaginary roots

500

The discriminant, number & type of root for

x^2 - 1/2x + 1/16 = 0

d = 0

1 real, rational root

solve by completing the square

100

Solve by completing the square.

x^2 -6x = 0

{ 0 , 6 }

200

Solve by completing the square.

x^2 + 6x + 2 = 0

{ - 3 + sqrt (7) , -3 - sqrt (7) }

300

Solve by completing the square.

x^2 - 3x - 40 = 0

{-5, 8 }

400

Solve by completing the square.

3x^2 + x - 10 = 0

{ -2, 5/3 }

500

Solve by completing the square.

9x^2 = 24x - 16

{ 4/3 }