How do you solve $5=sqrtx+1$ and check your solution?

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Answer 1 · 2017-07-27T02:16:57

See a solution process below:

Solution:

First, subtract $color(red)(1)$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$5 - color(red)(1) = sqrt(x) + 1 - color(red)(1)$

$4 = sqrt(x) + 0$

$4 = sqrt(x)$

Now, square both sides of the equation to solve for $x$ while keeping the equation balanced:

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

$16 = x$

$x = 16$

Check Solution:

Substitute $color(red)(16)$ into the original solution for $color(red)(x)$ and calculate both sides of the equation to ensure they are equal:

$5 = sqrt(color(red)(x)) + 1$ becomes:

$5 = sqrt(color(red)(16)) + 1$

Remember, the square root of a number produces both a positive and negative solution:

$5 = 4 + 1$ ** and ** $5 = -4 + 1$

$5 = 5$ ** and ** $5 = -3$

The check on the left shows our solution is correct.

The check on the right is an extraneous solution and can be ignored.

How do you solve 5=sqrtx+15=sqrtx+1 and check your solution?