Question

Using the method of completing, the Square solve +4x^2- 4√3x + 3 =0, leaving your answer in surd form​

Answer 1

Explanation:

4x^2 - 4 sqrt3 x + 3 = 0

To 'complete the square' the x^2 coefficient must be ' 1 ' ...so divide the entire equation by 4 to get ;

x^2 - sqrt 3 x + 3/4 = 0

Now, take 1/2 of the 'x' coefficient ( 1/2 sqrt3) , square it ( 3/4) and add it and subtract it from the equation

x ^2 - sqrt3 x + 3/4 - 3/4 + 3/4 = 0 reduce the 'square'

(x - sqrt(3)/2 )^2 = 0 <===== now solve for 'x'

x = sqrt(3)/2