Solve x^2 + (-1/2x + 5)^2 = 25

[Spruance]

How do we solve this equation:


x^2 + (-1/2x + 5)^2 = 25

Thanks in advance

 

[Doc Al]

Expand that squared term and you'll see that this quadratic equation simplifies nicely.

 

[HallsofIvy]

That's assuming that you mean ((-1/2)x + 5)^2 and not (-1/(2x)+ 5)^2.

 

[Spruance]

Thanks, then

x^2 + (-x/2 + 5)^2 = 25

x2 + x2/4 - 5x + 25 = 25

5x2/4 - 5x = 0 (* 4/5)

x2 - 4x = 0

x(x - 4) = 0

x = 0 or x = 4.