Solving Quadratic Equations: Factoring
What is the only solution of 2x2 + 8x = x2 - 16?
-4
The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring.
-420
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room.
2 3 5
What is the positive solution of x2 - 36 = 5x?
9
The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is true?
a
Two negative integers are 8 units apart on the number line and have a product of 308.
a
Two positive integers are 3 units apart on a number line. Their product is 108.
a
Which is a solution to (x − 2)(x + 10) = 13?
a
x2 + 6x = 40
a
A rectangle has an area of 40 square units. The length is 6 units greater than the width.
b
John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.
b
Which is a solution to the equation? (x −2)(x + 5) = 18
b
A group of students is given a 10 by 10 grid to cut into individual unit squares. The challenge is to create two squares using all of the unit squares. Their teacher states that after the two new squares are formed, one should have a side length two units greater than the other.
c
The product of two consecutive negative integers is 600. What is the value of the lesser integer?
c
Two positive integers have a product of 176. One integer is 5 less than the other integer. Which equation can be used to find the value of x, the greater integer?
c