MTH 95 Lesson 4 - Solving Quadratic Equations by Factoring with ApplicationsName:

1. Solve the following quadratic equations.

a. (x+ 2)(x− 10) = 0

b. x(x− 5)(x+ 4) = 0

c. 90(x+ 7)(9x− 5) = 0

d. x2 + 9x+ 8 = 0

e. x2 − 4x− 5 = 0

f. x2 + 4x = 21

g. x2 = 3x

h. 7x2 = −49x

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i. x2 − 2x+ 1 = 0

j. 36x2 = −60x− 25

k. 4x2 = −37x− 40

l. x(x− 6) = 16

m. (x− 1)(x+ 4) = −6

n. x(x− 4) = −(2x+ 1)

o. (x− 9)(x2 + 15x+ 50) = 0

p. x3 − 13x2 + 30x = 0

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2. Two numbers have a sum of −2 while their product is −35. What are the two numbers?

3. A rectangle’s base is 8 cm longer than its height. The area of this rectangle is 128 cm2. Whatare the dimensions of the rectangle?

4. A rectangle’s base is 2 inches shorter than five times its height. The rectangle’s area is 16inches squared. Find the rectangles dimensions.

5. There is a rectangular lot in the garden, with 6 ft in length and 4 ft in width. You plan toexpan the lot by an equal length around its four sides, and make the area of the expandedrectangle 48 square feet. How long should you expand the original lot in four directions?

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