This word problem might be easier to visualize if you'd please convert this wording into symbolic equations:
x^2 + y^2 = 4^2 (Note: This is the equation of a circle of radius 4 centered at the origin, (0,0).
y=x-2
Note that y^2 = x^2 - 4x + 4, so, after substituting this result into the first equation, we get
x^2 + (x^2 - 4x + 4) = 4^2
Simplifying, 2x^2 - 4x -12 = 0
Reduce this by dividing all terms by 2: x^2 - 2x - 6 = 0
Here the coefficients of this quadratic equation are 1, -2 and -6, or
a = 1, b = -2, c = -6
Insert these values into the quadratic formula. Solve the formula for x.
You MUST obtain 2 roots and check to ensure that each one is indeed a solution of the given equation.
Round off your results to the nearest tenth. Before you leave this problem, ask yourself whether there's just one root or there are two roots. How do you know that?
