Chapter 7

Solve. \((x+6)(x-3)=-8\)

Solve. \(16 p^{3}=24 p^{2}+9 p\)

Solve. \(m^{3}-2 m^{2}=-m\)

Solve. \(20 x^{2}-60 x=-45\)

Solve. \(3 y^{2}-18 y=-27\)

The product of two consecutive integers is 56. Find the integers.

The product of two consecutive integers is 42. Find the integers.

The area of a rectangular carpet is 28 square feet. The length is three feet more than the width. Find the length and the width of the carpet.

A rectangular retaining wall has area 15 square feet. The height of the wall is two feet less than its length. Find the height and the length of the wall.

A pennant is shaped like a right triangle, with hypotenuse 10 feet. The length of one side of the pennant is two feet longer than the length of the other side. Find the length of the two sides of the pennant.

Solve. \((x+8)(x-3)=0\)

Solve. \((3 y-5)(y+7)=0\)

Solve. \(p^{2}+12 p+11=0\)

Solve. \(q^{2}-12 q-13=0\)

Solve. \(m^{2}=6 m+16\)

Solve. \(4 n^{2}+19 n=5\)

Solve. \(a^{3}-a^{2}-42 a=0\)

Solve. \(4 b^{2}-60 b+224=0\)

The product of two consecutive integers is \(110 .\) Find the integers.

The length of one leg of a right triangle is three feet more than the other leg. If the hypotenuse is 15 feet, find the lengths of the two legs.

Area of a patio If each side of a square patio is increased by 4 feet, the area of the patio would be 196 square feet. Solve the equation \((s+4)^{2}=196\) for s to find the length of a side of the patio.

A watermelon is dropped from the tenth story of a building. Solve the equation \(-16 t^{2}+144=0\) for \(t\) to find the number of seconds it takes the watermelon to reach the ground.

Give an example of a quadratic equation that has a GCF and none of the solutions to the equation is zero.