you can solve all of these problems using the formula for the roots of a quadratic equation given in the following general form:

p(x) = a*x^2 + b*x + c

X1 = (-b + sqrt(b^2 - 4*a*c)) / (2*a)

X2 = (-b - sqrt(b^2 - 4*a*c)) / (2*a)

the discriminant is defined as

delta = b^2 - 4*a*c

if delta equals zero there is one root with a multiplicity of two, if it's negative then the roots are complex and if it's positive the roots are real

let's denote the length of the piece used for creating the square as x, and that used for creating the circle as y.A wire 370 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire

obviously -> x+y = 370

the area of the square is (x/4)^2

the perimeter of the circle is 2*pi*r = y, and we know that it's area is pi*r^2

thus we can express it's area using y as follows: pi*(y / 2*p)^2

now we are told that both of the figures have the same area thus: (x/4)^2 = pi*(y / 2*p)^2

which leaves us with two equations in two unknowns:

x + y = 370

(x/4)^2 = pi*(y / 2*p)^2

I think that you'll be able to continue from here...