How do you solve $sqrt(x)= 2x$ ?

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Answer 1 · 2017-02-27T19:02:07

See the entire solution process below:

First, square each side of the equation:

$(sqrt(x))^2 = (2x)^2$

$x = 4x^2$

Next, subtract $color(red)(x)$ from each side of the equation:

$x - color(red)(x) = 4x^2 - color(red)(x)$

$0 = 4x^2 - x$

$4x^2 - x = 0$

Then, factor an $x$ out of each term on the left side of the equation:

$x(4x - 1) = 0$

Now, solve each term for $0$ to find all the solutions to the problem:

Solution 1)

$x = 0$

Solution 2)

$4x - 1 = 0$

$4x - 1 + color(red)(1) = 0 + color(red)(1)$

$4x - 0 = 1$

$4x = 1$

$(4x)/color(red)(4) = 1/color(red)(4)$

$(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 1/4$

$x = 1/4$

The solution is: $x = 0$ and $x = 1/4$

How do you solve sqrt(x)= 2xsqrt(x)= 2x?