SOLUTION: hi these question are from a worksheet....plzz kindly help 1) A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the law

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: hi these question are from a worksheet....plzz kindly help 1) A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the law      Log On


   

Question 204190: hi these question are from a worksheet....plzz kindly help
1) A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and flower bed is 165m². What is the width of the flower bed?
Let x be the width of the flowerbed
(8+2x)(4+2x)=165
2) Can x (x – 5) = 0 be solved by dividing both sides of the equation by x?
Explain your answer.

3)Write a quadratic equation whose roots are 5 and –3.


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1)
Starting with:
%288%2B2x%29%284%2B2x%29+=+165 Expand and rearrange the left side.
4x%5E2%2B24x%2B32+=+165 Subtract 165 from both sides.
4x%5E2%2B24x-133+=+0 Solve this quadratic equation using the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a where: a = 4, b = 24, and c = -133.
x+=+%28-24%2B-sqrt%2824%5E2-4%284%29%28-133%29%29%29%2F2%284%29
x+=+%28-24%2B-sqrt%28576-%28-2128%29%29%29%2F8
x+=+%28-24%2B-sqrt%282704%29%29%2F8
x+=+%28-24%2B52%29%2F8 or x+=+%28-24-52%29%2F8
highlight%28x+=+3.5%29 or cross%28x+=+-9.5%29 Discard the negative solution as the width of the flower bed can only be a positive quantity.
The width of the flower bed is 3.5 feet.
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2) Can x%28x-5%29+=+0 be solved by dividing both sides by x?
No, because you would get olny one of the solutions to this quadratic equation when, in fact, there are really two solutions!
Here's how you would solve it:
x%28x-5%29+=+0 Apply the zero product rule: If a%2Ab+=+0 then either a+=+0 or b+=+0 or both.
highlight%28x+=+0%29 or x-5+=+0
If x-5+=+0 then highlight_green%28x+=+5%29
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3) Write a quadratic equation whose roots are:
x+=+5 and x+=+-3 If these are the roots, then the factors are:
x-5+=+0 and x%2B3+=+0 Multiply these two factors together to get the original quadratic equation.
y+=+%28x-5%29%28x%2B3%29 Multiply using FOIL.
y+=+x%5E2%2B3x-5x-15 Simplify.
highlight%28y+=+x%5E2-2x-15%29