Question

Martha sells custom painted square canvases. She determined that the amount of tissue paper she'll need to wrap each canvas can be represented by
y= x^2 + 2x + 1, where y is the total square inches of tissue paper and x is the side length of the canvas in inches. Write and solve an equation to determine the side length of the canvas is Martha needs 49 square inches of tissue paper.

Answer 1

Given:

The equation is

$y=x^2+2x+1$

where y is the total square inches of tissue paper and x is the side length of the canvas in inches.

To find:

The side length of the canvas is Martha needs 49 square inches of tissue paper.

Solution:

We have,

$y=x^2+2x+1$

Putting y=49, we get

$49=x^2+2x+1$

$0=x^2+2x+1-49$

$0=x^2+2x-48$

Splitting the middle term, we get

$0=x^2+8x-6x-48$

$0=x(x+8)-6(x+8)$

$0=(x+8)(x-6)$

Using zero product property, we get

$x+8=0$ and $x-6=0$

$x=-8$ and $x=6$

Side length cannot be negative. So, only possible value of x is 6.

Therefore, Martha needs 6 inches side length of the canvas for 49 square inches of tissue paper.