SOLUTION: I am having trouble with the following question, please help. {{{sqrt(16x-4)= 4x-2}}} solve for x

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Question 425925: I am having trouble with the following question, please help.
solve for x
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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 =

substitute in this equation to get x =

simplify to get x =

this can be reduced to

this an be further reduced to

this can be further reduced to

note that = = =