Solve the equation.

Question

Solve the equation

 

x+2=√(28-x)

 

Please help me I would really appreciate it. Thank you! :)

Answer 1

x + 2 = √(28 - x)

(x + 2)² = 28 - x

x² + 4x + 4 = 28 - x

 

Can you solve for x?

Answer 2

Hi Chloe,

 

Square both sides to get:

 

(x + 2)^2 = 28 - x

 

Expand:

 

x^2 + 4x + 4 = 28 - x

 

Simplify:

 

x^2 + 5x - 24 = 0

 

Factor:

 

(x + 8)(x - 3) = 0

 

Solve:

 

x = -8 or 3

 

Check your work:

 

x = -8 → -6 = √[36] ? NO

 

x = 3 → 5 = √[25] ? YES

 

Hope this helps!

Answer 3

If the entire expression (x - 28) is under the square root sign, then let's begin by squaring both sides.

 

(x + 2)² = 28 - x

 

x² + 4x + 4 = 28 - x

 

x² + 5x - 24 = 0

 

(x - 3)(x + 8) = 0

 

x = 3 and x = -8

 

We have to plug each value back into the original equation to verify that each are indeed solutions.

 

3 + 2 = √(28 - 3)

 

5 = √25

 

5 = 5

 

Now, try x = -8.

 

-8 + 2 = √(28 - (-8))

 

-6 = √36

 

-6 ≠ 6

 

Therefore, the only solution is x = 3