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

Solution:

Given: Square root of x plus 10 end root minus 4 equals x

It can be mathematically written as

√(x + 10) - 4 = x

√(x + 10) = x + 4

By squaring on both sides

(x + 10) = (x + 4)²

Let us expand it using the algebraic identity (a + b)² = a² + b² + 2ab

x + 10 = x² + 8x + 16

x² + 7x + 6 = 0

By splitting the middle term

x² + x + 6x + 6 = 0

Taking out the common terms

x(x + 1) + 6(x + 1) = 0

(x + 1)(x + 6) = 0

x = -1 or x = -6

Let us substitute x = -6 in the equation

√(-6 + 10) - 4 = √4 - 4 = 2 - 4 ≠ -6

x = -6 is an extraneous solution.

Therefore, the solution is x = -1.

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

Summary:

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