help! (30-2x)(20-2x)=400?

Question

any thoughts???

Answer 1

(30 - 2X)(20 - 2X) = 400
600 -60X - 40X + 4X^2 = 400
200 -100X + 4X^2 = 0
4[(50 - 25X + x^2] = 0
Using 'Completing the Square' eq'n
x = (--25 +/-sqrt[25^2 - 4(1)(50)])/2(1)
x = (25 +/-sqrt[625 - 200])/2
x = (25 +/-sqrt425)/2
x = (25 +/- 20.6155)/2
x = (25 + 20.6155)/2 = 22.8078
&
x = (25 - 20.6155)/2 = 2.1922

So 'x' = two values - 22.8078 & 2.1922

Answer 2

A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path?
:
Draw diagram of this; label the outside dimensions of the rectangle 30 by 20.
Label the width of the path as x, it will be apparent that the dimensions of
the garden (inside the path), will be (30-2x) by (20-2x)
:
The area of the garden is given as 400 sq/ft
:
A simple area equation:
:
length times width = 400 sq/ft
(30-2x) * (20-2x) = 400

Answer 3

This is a quadratic equation in x, expand the left hand side out,

600 - 100x + 4x^2 = 400
4x^2 -100x + 200 = 0
x^2 - 25x + 50 = 0
and now use the quadratic formula, you will have two solutions
1/2 * (25 +- sqrt(425) )

Answer 4

30-2x=400 or 20-2x=400
-2x=370 or -2x=380, calculate

Answer 5

(30 - 2x)(20 - 2x) = 400
600 - 60x - 40x + 4x² = 400
200 - 100x + 4x² = 0
4x² - 100x + 200 = 0
4(x² -25x + 50) = 0