Question 425925
sqrt(16x-4) = 4x-2


square both sides to get:


16x-4 = (4x-2)^2


expand to get:


16x-4 = 16x^2 - 16x + 4


subtract 16x - 4 from both sides of the equation to get:


0 = 16x^2 - 32x + 8


commute to get:


16x^2 - 32x + 8 = 0


divide both sides of equation by 8 to get:


2x^2 - 4x + 1 = 0


use quadratic formula to get:


x = 1 +/- (sqrt(2)/2)


confirm by substituting in original equation to see if the equality holds.


original equation is:


sqrt(16x-4) = 4x-2


easiest way is to use your calculator to get the value of 1 +/- (sqrt(2)/2 and store it in memory for future use.


i get x = 1.707106781... or x = .292893219... which i stored in memory.


then i substituted 1.707106781... for x to get 4.828427125 = 4.8328427125 which is true, confirming that value for x is good.


then i substituted .292893219... for x to get sqrt(.686291501...) = -.8284271254...


if i square both sides of this equation, i get:


.686291501... = .686291501..., confirming that the value of x = .292893219... is also good.


i did not solve the quadratic formula for you, but you can do it yourself by following these rules.


the standard form of a quadratic equation is ax^2 + bx + c = 0


your equation is 2x^2 - 4x + 1 = 0


that makes:


a = 2
b = -4
c = 1


the quadratic formula is x = {{{((-b) +- sqrt(b^2-4ac))/(2a)}}}


substitute in this equation to get x = {{{((-(-4)) +- sqrt((-4)^2-4*2*1))/(2*2)}}}


simplify to get x = {{{(4 +- sqrt(8))/4}}}


this can be reduced to {{{(1 +- (sqrt(8))/4)}}}


this an be further reduced to {{{(1 +- (2*sqrt(2))/4)}}}


this can be further reduced to {{{1 +- (sqrt(2)/2)}}}


note that {{{sqrt(8)}}} = {{{sqrt(4*2)}}} = {{{sqrt(4)*sqrt(2)}}} = {{{2*sqrt(2)}}}