Question 118878


{{{16x^2 - 16x + 4 > 0}}}…..divide both sides by {{{4}}}

{{{4x^2 - 4x + 1> 0}}}…..

Solve it as an {{{equation}}} first:

{{{4x^2 - 4x + 1= 0}}}…..

Use quadratic formula to solve for {{{x}}}

{{{x[1,2]=(-b +- sqrt (b^2 - 4*a*c )) / (2*a)}}}


{{{x[1,2]=(-(-4) +- sqrt ((-4)^2 - 4*4*1 )) / (2*4)}}}


{{{x[1,2]=(4 +- sqrt (16 - 16 )) / 8}}}


{{{x[1,2]=(4 +- sqrt (0 )) / 8}}}


{{{x[1,2]=(4 +- 0) / 8}}}…………there is only one solution


{{{x[1]=4 / 8}}}


{{{x[1]=1 / 2}}}


So, your solution will be: 


{{{x > 1/2}}} or ({{{1/2}}},{{{infinity}}})


Graph it, and {{{shade}}} everything to the right from 

{{{x=1/2}}} excluding {{{x=1/2}}}



*[invoke solve_quadratic_equation 4, -4, 1]