The area of a rectangular piece of fencing is represented by the equation w(4w+4)=3, where w is the width of fencing in yards. Find the width of the fencing.
first solve out parenthesis and bring the 3 to the other side which will give you 4w^2+4w-3=0 factoring the polynomial will give you (w-2) and (w+4) set them both to zero and solve it and then plug each answer back into the original polynomial to see if they equal zero if they do that is your answer but if one of them doesnt then that wont be your answer
oh yea i didn't factor out correctly so yea im too lazy to figure out the correct factor so you can do that yourself
yeah. It's (2w+3)(2w-1), so w=1/2 or -3/2
lol thanks steve when i was doing it i completelyforgot about the 4 in front of the 4w^2
To find the width of the fencing, we need to solve the equation w(4w+4) = 3.
1. Start by distributing the w to both terms inside the parentheses:
w(4w + 4) = 3
4w^2 + 4w = 3
2. Rewrite the equation in standard quadratic form:
4w^2 + 4w - 3 = 0
3. Set the equation equal to zero:
4w^2 + 4w - 3 = 0
4. This is now a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use factoring:
The factors of 4w^2 are (2w)(2w).
The factors of -3 are (-3)(1) or (3)(-1).
We need to find two numbers that multiply to give -3 and add up to 4. The numbers are 3 and -1.
So, we can rewrite the equation as:
(2w + 3)(2w - 1) = 0
5. Now, set each factor equal to zero and solve for w:
2w + 3 = 0 or 2w - 1 = 0
For the first equation:
2w = -3
w = -3/2
For the second equation:
2w = 1
w = 1/2
Therefore, the possible values for the width of the fencing are w = -3/2 or w = 1/2.
Note: Since it doesn't make sense to have a negative width for a fence, we discard the solution w = -3/2. The valid solution is w = 1/2, which means the width of the fencing is half of a yard.