Question

Factorising and solving quadratics

Answer 1

x^2 + 12x - 220 = 0

(x + 22)(x - 10) = 0

x = -22, x = 10

Dimensions:

4 cm, 11 cm, and 21 cm

Answer 2

Answer:

4cm, 11cm, 21cm

Step-by-step explanation:

Hello!

Let's first factor the Quadratic by grouping. Find two numbers that add up to 12 but multiply to -220.

Those two numbers are 22 and -10. Expand 12x to 22x and -10x.

Factor by Grouping

• $x^2 + 12x - 220 = 0$
• $x^2 +22x-10x-220=0$
• $x(x+22)-10(x+22)=0$
• $(x - 10)(x+22) = 0$
• $x = 10, x = -22$

There are two solutions for the quadratic, but only one works because you can't have a negative measure for a length.  The term for this occasion is called an Extraneous Solution. So we are only going to use 10 for x to find the sides.

Plug in x in each side length.

• 10 + 1 = 11
• 10 + 11 = 21

The side lengths are 4, 11, and 21.