Download Algebra Name 9.7 Solving Problems with Quadratic Equations Solve

Algebra
9.7 Solving Problems with Quadratic Equations
Solve the following problems algebraically.
1. If a number is added to its square, the result is 72.
Find the number. (Hint: there are 2 possibilities.)
2. If a number is subtracted from its square, the result
is 90. Find the number.
3. A positive number is 56 less than its square.
Find the number.
4. A negative number is 56 less than its square.
Find the number.
5. Find two consecutive negative integers whose
product is 72.
6. Find two consecutive positive even integers
whose product is 120.
7. Find two consecutive negative odd integers
whose product is 195.
8. Find three consecutive positive integers such
that the product of the second and third integers
is one less than 7 times the first integer.
9. The sum of two numbers is 15. The product of
the numbers is 54. Find the numbers.
10. The sum of the squares of two consecutive
positive odd integers is 202. Find the integers.
Name
11. The sum of the squares of two consecutive
negative odd integers is 130. Find the integers.
12. The length of a rectangle is 5 m greater than the
width. Find the dimensions of the rectangle if
its area is 126 m2.
13. The length of a rectangle is 8 cm less than twice
the width. Find the dimensions of the rectangle
if its area is 120 cm2.
14. Originally the dimensions of a rectangle were 12 cm
by 7 cm. When both dimensions were decreased by
the same amount, the area of the rectangle decreased
by 34 cm2. Find the dimensions of the new rectangle.
15. Originally the dimensions of a rectangle were 17 cm
by 8 cm. When both dimensions were decreased by
the same amount, the area of the rectangle decreased
by 66 cm2. Find the dimensions of the new rectangle.
16. Originally a rectangle was twice as long as it was wide.
When 5 m was subtracted from its length 3 m subtracted
from its width, the new rectangle had an area of 55 m2.
Find the dimensions of the new rectangle.
17. A rectangular garden measuring 12 m by 16 m is to have
a walkway installed around it with a width of x meters.
Together, the walkway and the garden have an area of
396 m2. Find the width of the walkway.
18. A homeowner wants to increase the size of a rectangular
deck that now measures 15 feet by 20 feet. If the length
and the width are increased by the same number of feet
the new deck has an area of 500 square feet. Find the
number of feet that the deck is increased by.