Solving Quadratics

Square Roots

100

x² + 7 = 88

What is x = 9, x = -9?

200

-5x² = -500

What is x = 10, x = -10?

300

8x² - 7 = 193

What is x = 5, x = -5

400

- 4x² = -300

What is

x = +- 5sqrt(3)

500

4x² + 1 = 401

What is x = 10, x = -10?

Completing the Square

100

x² +4x = 12

What is x = 2, x = -6?

200

x² +8x = 65

What is x = 5, x = -13?

300

x² - 12x + 23 = 0

What is 

 x = 6 +- sqrt(13) 

400

x² - 10x + 26 = 8

What is  x = 5 +- sqrt(7) 

500

x² + 2x = -20

What is no solution?

Factoring

100

x^2+5x+4=0

x = -1 and x = -4

200

x^2+6x-40=0

x = -10 and x = 4

300

x^2-3x+2=0

x = 1 and x = 2

400

x^2+9x-36=0

x = -12 and x = 3

500

x^2-x-110=0

x = -10 and x = 11

Any Method

100

x^2+6x=16

x = -2 and x = 8

200

x^2+4=0

No Solution

300

x^2-40=0

x = +- 2sqrt10

400

x^2+8x-55=10

x = -13 and x = 5

500

x^2+5x+4=5x+4

x = 0

Word Problems (x2 Points)

100

The product of two consecutive even integers is 168. Find the integers.

(12 and 14) or (-12 and -14)

200

The sides of a square are increased by 3m. This causes the area to be 64 square meters. What was the original side length?

5 meters

300

The length and width of a rectangular garden were 4m and 5m. Each were increased by the same amount. The new area of the garden is 56 square meters. Find the new dimensions. (Hint: let x by the amount of increase).

7m and 8m

400

The width of a rectangle is 2 m less than the length. The area is 48 square meters . Find the dimensions.

6 m  by 8 m

500

The base of a triangle is 4 cm shorter than the height. The area is 30 cm2 . Find the base and the height of the triangle.

b = 6 cm and h = 10 cm