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How do you solve #x + 2 = sqrt(7 x) + 2#?

Answer 1

Nathan Axel

#x=0# and #x=7#

#x+2=sqrt(7x)+2#

Subtract 2 on both sides

#=> x=sqrt(7x)#

Square Both Sides

#x^2=7x#

divide by #x# on both sides (assuming #x != 0#)

#=> x=7#

However, we must check if #x=0# is a solution

#0+2=sqrt(7*0)+2#

#=> 2=0+2#

This is true, so #x=0# is a solution!

Thus, #x=0# and #x=7#

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Answer 2

Julia Adams

To solve the equation x + 2 = sqrt(7x) + 2, we can start by subtracting 2 from both sides of the equation to isolate the square root term. This gives us x = sqrt(7x).

Next, we can square both sides of the equation to eliminate the square root. This gives us x^2 = 7x.

Rearranging the equation, we have x^2 - 7x = 0.

Factoring out an x, we get x(x - 7) = 0.

Setting each factor equal to zero, we have x = 0 and x - 7 = 0.

Solving for x, we find x = 0 and x = 7 as the solutions to the equation x + 2 = sqrt(7x) + 2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.