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Write boarder calculated

A quilt is three feet by six feet. If there is 22 square feet of fabric available to use as a border around the quilt, how wide should the border be? Assume all of the fabric must be used. Referring to the model below, the red rectangle represents the quilt, the blue region represents the border around the quilt. So because the quilt is three feet by six feet, this length is three feet, and this length is six feet. And now we don't know the width of the border, but it is of uniform width. Let's have X equal the width of the border, which means this length is X feet, and so is this length, at each corner. And now as we're going to terming the dimensions of the outer rectangle, or the quilt, including the border. If this length is three, and this length is X, and this length is X, this outer length must be three, plus X, plus X, or three, plus two X feet. This length here must be six, plus X, plus X, or six, plus two X feet. From here, we're going to term in the area of the border, but a terming the area of the outer rectangle, and subtracting the area of the inner rectangle. And this area must be equal to the 22 square feet of fabric that is used for the border. And because the area of a rectangle's equal to length times width, the area of the outer rectangle, or the area of the quilt and the border, must be equal to the quantity six plus two X, times the quantity three plus two X. So this gives us the area of the quilt and the border, or the area of the outer rectangle. And now we want to subtract the area of the quilt, or the area of the inner rectangle, which would be three times six. This leaves us with the area of the border, which must equal 22 square feet. Therefore, this is equal to 22. Now if we solve this equation for X, we can determine the width of the border. For the first step, let's (mumbles) the parenthesis on the left side. When multiplying two binomials, we always have four products. We first distribute the six, then distribute the two X. Six times three equals 18. Six times two X equals 12 X. So we have plus 12 X. And now we distribute two X. Two X times three equals six X, which gives us plus six X. And two X times two X equals four X squared, Which gives us plus four X squared. And we have minus three times six, which gives us minus 18 equals 22. And now we simplify the left side of the equation. 18 minus 18 is equal to zero. We have four X squared. 12 X plus six X equals 18 X. So plus 18 X, equals 22. Notice how we have a quadratic equation....