How do you solve sqrt(x^2+2)-5=0?

2 Answers
Aug 20, 2017

x=sqrt23, x=-sqrt23

Explanation:

sqrt(x^2+2) - 5 = 0

Add 5 to each side:
sqrt(x^2+2) = 5

Square each side:
x^2+2 =25

Subtract 2 from each side:
x^2 = 23

color(blue)(x= +- sqrt23)

Aug 20, 2017

See a solution process below:

Explanation:

First, add color(red)(5) to each side of the equation to isolate the radical while keeping the equation balanced:

sqrt(x^2 + 2) - 5 + color(red)(5) = 0 + color(red)(5)

sqrt(x^2 + 2) - 0 = 5

sqrt(x^2 + 2) = 5

Next, square each side of the equation to eliminate the radical while keeping the equation balanced:

(sqrt(x^2 + 2))^2 = 5^2

x^2 + 2 = 25

Then, subtract color(red)(2) from each side of the equation to isolate x^2 while keeping the equation balanced:

x^2 + 2 - color(red)(2) = 25 - color(red)(2)

x^2 + 0 = 23

x^2 = 23

Now, take the square root of each side of the equation to solve for x while keeping the equation balanced. Remember, the square root of a number produces both a positive and a negative result:

sqrt(x^2) = +-sqrt(23)

x = +-sqrt(23)