Question

What is the solution of 4x^2+1>=4x



(answer should be in [ or ) possible an "and" or an "or"

Answer 1

When dealing with quadratics, it helps to make it equal zero so we first subtract 4x from both sides:

4x^2+1 >= 4x
4x^2-4x+1 >= 0
4(x^2-x)+1 >= 0 (Factor out the 4)
4(x-0.5)^2 >= 0 (Write in completed square format)
(x-0.5)^2 >= 0 (Divide both sides by 4)

Taking the square root of both sides gives us two answers:

+(x-0.5) >= 0
So x >= 0.5

-(x-0.5) >= 0
So x <= 0.5

So we know x >= 0.5 OR x <= 0.5. Therefore x is any real number :)