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x=position, v=velocity, a=acceleration, t=time.
equation of position: x=vt+(1/2)at^2, or
(1/2)(at^2)+vt-x=0
complete the square, and
t=(-v+/-sqrt((2ax)+v^2))/a
general form of quadratic equation: a(x^2)+bx+c=0
complete the square, and
x=(-b+/-sqrt((b^2)-4ac))/2a
Quadratic Equations In General:
The area of a rectangle is 100. The length is equal to 5 more than 4 times the width. What is the length and what is the
width?
That is: (4w+5)w=100 where w= width, l=(4w+5), l=length
4(w^2)+5w-100=0
Complete the square and you have w. Use A=wl to find l (A=area).
The area, A, of a right triangle is known. So is the hypotenuse, h. What are the legs, a and b?
A=(1/2)ab and h^2=(a^2)+(b^2)
a^4-(h^2)(a^2)+4A^2=0
(a^2- (h^2)/2)^2=((h^4)-16A^2)/4
a^2=...
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