Solving quadratic equations: factoring

Two negative integers are 5 units apart on the number line, and their product is 126. What is the sum of the two integers?

-23

What are the solutions of the equation 4x2 + 3x = 24 - x?

-3 or 2

The expression n2 + n represents the total number of blocks used in the nth figure of a pattern. Use the equation n2 + n = 56 to determine which figure has 56 blocks.

Figure 7 has 56 blocks.

Percy solved the equation x2 + 7x + 12 = 12. His work is shown below. Is Percy correct? Explain. 1. (x + 3)(x + 4) = 12 2. x + 3 = 12 or x + 4 = 12 3. x = 9 or x = 8

Percy is not correct because he applied the zero product property to a factored expression that was not equal to 0. He should have subtracted 12 from both sides to get x2 + 7x = 0 before factoring. The correct solutions are 0 and -7.

A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two congruent right triangles with areas of 44 square inches. Which statements are true? Check all that apply.

The area of the rectangle is 88 square inches. The equation x2 - 3x - 88 = 0 can be used to solve for the length of the rectangle. The triangle has a base of 11 inches and a height of 8 inches.

Which statement is true about the equation (x - 4)(x + 2) = 16?

The factored form of the equation is (x + 4)(x - 6) = 0.

Complete the equivalent equation for -7x - 60 = x2 + 10x. (x +5 )(x +12 ) = 0 What are the solutions of -7x - 60 = x2 + 10x?

x = -12 or -5

The product of two consecutive integers is 72. The equation x(x + 1) = 72 represents the situation, where x represents the smaller integer. Which equation can be factored and solved for the smaller integer?

x2 + x - 72 = 0