Factoring
Quadratic Formula
Complete the Square
Solve using Square Roots
Word Problems
Expression
100
x^2+5x=0
x=-5 and x=0
100

-9x^2-6x-1=0

x=-1/3

100
Fill in the blank to complete the square: x^2-6x+____
9
100
3x^2=108
x=6 and x=-6
100

The product of two consecutive integers is 90.  What is one possible pair of integers?

9 and 10 OR -10 and -9

200
k^2+12k-45=0
k=-15 and k=3
200
x^2+4x-3=0
x=-2+√7 and x=-2-√7
200
Fill in the blank to complete the square: x^2+10x+____
25
200
5y^2+4=14
x=√2 and x=-√2
200
The product of two consecutive even integers is 195.  Find the pair of positive integers that satisfy this condition.

13 and 15

300

3x^2-24x+48=0

x=4

300
3x^2+6x+2=0
x=(-3+√3)/3 and x=(-3-√3)/3
300
Fill in the blank to complete the square: x^2+9x+____
81/4
300
3(p+1)^2=81
x=-1+3√3 and x=-1-3√3
300

The length of a rectangle is 5 inches more than twice a number.  The width is 4 inches less than the same number.  If the area of the rectangle is 15, find the number.

5

400
4x^2-20x+25=0
x=2.5
400
2x^2-5x+8=0
x=(5+i√39)/4 and x=(5-i√39)/4
400
x^2-8x+13=0
x=4+√3 and x=4-√3
400
4(x-7)^2=80
x=7+2√5 and x=7-2√5
400

The ages of three family children can be expressed as consecutive integers.  The square of the age of the youngest child is 4 more than eight times the age of the oldest child.  Find the ages of the three children.

10,11,12
500
20a^2-13a-21=0
a=-.75 and a=1.4
500
6x^2-8x+3=0
x=(4+i√2)/6 and x=(4-i√2)/6
500
x^2-6x-15=0
x=3+2√6 and x=3-2√6
500
2(x+8)^2=108
x=-8+3√6 and x=-8-3√6
500

Collin is building a deck on the back of his house.  He has enough lumber for the deck to be 144 square feet.  The length should be 10 feet more than its width.  What should the dimensions of the deck be?

8 x 10

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