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.