# Identify all the solutions of the square root of x plus 10 end root minus 4 equals x.

Squares and square roots are very interesting concepts that have many applications. Squares are basically any number raised to the power 2 and a square root is a number raised to the power 1/2.

## Answer: The solution of the square root of x plus 10 end root minus 4 equals x is x = -1.

Let's understand the solution in detail.

**Explanation:**

Given equation: √(x + 10) - 4 = x.

Now:

⇒ √(x + 10) = x + 4

⇒ (x + 10) = (x + 4)^{2} [Squaring both the sides]

⇒ x + 10 = x^{2} + 8x + 16 [expanding using the identity of (a + b)^{2}]

⇒ x^{2} + 7x + 6 = 0

⇒ x^{2} + x + 6x + 6 = 0

⇒ x(x + 1) + 6(x + 1) = 0

⇒ (x + 1)(x + 6) = 0

Hence, we get x = -1 or x = -6 as solutions.

But, after putting x = -6 in the original equation, we get:

⇒ √(-6 + 10) - 4 = √4 - 4 = ±2 - 4 = -6 or -2

Hence, we are not getting a perfect solution using x = -6. Hence, it is an extraneous solution.