The length of a rectangle is (2x -1) and width (x+3), given that the area is 294cm^2 , determine the value of x. I've attempted using
x=−b±√b2−4ac/2a, The answer is supposed to be x=11.
2x^2 +5x-3Okay, so the area is the product of the width and the height:
[MATH]A(x)=(2x-1)(x+3)[/MATH]
Can you expand that to get this in the form required for part a) of the question?
2x^2 +5x-3
Okay. I tried..I don't know if I'm going correct( if it's even the right way...) or how to continue.Yes, so now equate this to 294, and then solve for \(x\):
[MATH]2x^2+5x-3=294[/MATH]
[MATH]2x^2+5x-297=0[/MATH]
Can you now factor?
x=11 THANK You. It always seems easy after I understand it... Then I ask, "Why did I not understand in the first place?"Okay, if you're using the quadratic formula, then you want:
[MATH]x=\frac{-5\pm\sqrt{2401}}{4}[/MATH]
Now, 2401 is a perfect square. We should be able to easily see that:
[MATH]50^2=2500[/MATH]
Hence:
[MATH]49^2=(50-1)^2=50^2-2\cdot50+1=2500-99=2401[/MATH]
And so, we would find (after discarding the negative root since it will lead to negative measures of length):
[MATH]x=\frac{-5+49}{4}=\,?[/MATH]
Oh. I see the error, ( just fixed it ) but no, I had it as b^2 in my book, only made a typo on here, I just didn't understand. ^-^Please note that you listed the quadratic formula incorrectly. Maybe that is why you were getting the wrong answer. Do you see why your formula is wrong?
… using
x=−b±√b^2−4ac/2a, ...
Adding to lookagain's comments: Yes -- without the grouping symbols, someone unfamiliar with the formula might read your typing as:-b±√b2−4ac/2a