How do you solve #2sqrt(x+2)-3=7#?

Answer 1

#x=23#

Given:

#2 sqrt(x+2)-3 = 7#
Add #3# to both sides to get:
#2 sqrt(x+2) = 10#
Divide both sides by #2# to get:
#sqrt(x+2) = 5#

Square both sides (keeping in mind that doing so may result in erroneous answers) to obtain:

#x+2 = 25#
Subtract #2# from both sides to get:
#x = 23#

Check:

#2 sqrt(23+2) - 3 = 2 sqrt(25)-3 = (2*5)-3 = 10 - 3 = 7#
#color(white)()# Notes

Why is squaring both sides of the equation a cause for concern?

When you square both sides of an equation, solutions of the resulting equation may not be solutions of the original, due to having different signs. The function #f(x) = x^2# maps positive and negative values to the same value.

For instance, if you owned

#sqrt(x+2) = -5#

then both sides squared would result in:

#x+2 = 25#

and thus:

#x=23#
but we have #sqrt(23+2) = 5 != -5#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To solve the equation 2√(x+2) - 3 = 7, you can follow these steps:

  1. Add 3 to both sides of the equation: 2√(x+2) = 10.
  2. Divide both sides by 2: √(x+2) = 5.
  3. Square both sides of the equation: x + 2 = 25.
  4. Subtract 2 from both sides: x = 23.

Therefore, the solution to the equation is x = 23.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

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.

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7