Quadratic word problem 2?

Question

A rectangular plot of land measures 24 meters by 40 meters. If the Department of Public Works covers the perimeter of this land with a sidewalk of uniform width, the area of exposed land shrinks to 665 square meters. How wide is the sidewalk?
well, my concept is, to slove it with Quadratic equation.
(40-2x)(24-2x)=665
then I get 4x^2-128x+295=0
but then I can't factor it out. please give me a better vision on this problem.

Answer 1

Upto the stage 4x^2-128x+295=0 you have done it perfectly OK
So I am starting from the next step
=>4x^2-118x-10x+295=0
=>2x(2x-59)-5(2x-59)=0
=>(5x-59)(2x-5)=0
Therefore, either 5x-59=0 or 2x-5=0
Rejecting 5x-59=0 in which value of x will be big enough to cover the whole of breadth of the land,we accept that 2x-5=0
Or,2x=5
or x=2.5 m

Answer 2

a million. Do you have a typo? The sq. of two consecutive integers won't be able to be even. the version is often equivalent to the sum of the two integers (2^2, 3^2 - distinction = 2+3; 3^2, 4^2 - distinction = 3 +4; etc). a wierd and an excellent constantly equivalent a wierd. If the 0.33 is seventy six extra beneficial than the 1st, then, based on the previous paragraph, the version between the 1st and 2d is (x + x+a million) and the version between the 2d and 0.33 is (x + a million + x + 2). blended, you have 4x + 4 = seventy six. fixing, you get 18, 19, 20. Edit: possibly it would help if I discovered to study. on condition that the two integers that meet the factors are 18 and 20, and that they are the 2d and 0.33 integers interior the question, the respond is sixteen, 18, and 20 (like all different men pronounced). 2. l is length, w is width. l = w + 3, plus the border. because of the fact the border is all over the image, that's on the two factors and must be further into the size two times. In different words, the size is w + 3 + 2*2 The width has an identical border, so that's equivalent to w + 2*2 section is comparable to length circumstances width and you realize the respond is 108, so 108 = (w + 3 + 4)(w + 4) 108 = (w + 7)(w + 4) 108 = w^2 + 11w + 28 0 = w^2 + 11w - eighty ingredient to get: 0 = (w + sixteen)(w - 5) The width won't be able to be -sixteen, so it would desire to be 5 inches. That measn the size might desire to be 8 inches.

Answer 3

Using the quardratic formula, we get

(-b ± √b² - 4ac)/2a

= (-(-128) ± √128² - 4(4)(295))/2(4)

= (128 ± √16384 - 4720)/8

= (128 ± √11664)/8

= (128 ± 108)/8

= 20/8, 236/8

= 2.5, 29.5

Answer 4

Simplifying
4x2 + -128x + 295

Reorder the terms:
295 + -128x + 4x2

Factor a trinomial.
(5 + -2x)(59 + -2x)

Final result:
(5 + -2x)(59 + -2x)

Answer 5

x = [-b + (b2 -4ac)^1/2] / 2a and [-b - (b2 -4ac)^1/2] / 2a

x = 128 + ( 16384 - 4720 ) ^1/2 /8
x= 128 + 108 / 8 and 128 -108 / 8

x= 29,5 and 2,5
the answer is 2,5

Answer 6

do it in the quadratic formula x = [ -b ± sqrt(b^2 - 4ac) ] / 2a