# Identify all of the following solutions of square root of x plus 14 end root plus 2 equals x.

x = -6, x = -1, x = -6 and x = -1, None of the above

**Solution:**

Given: Square root of x plus 14 end root plus 2 equals x

It can be mathematically written as

√(x + 14) + 2 = x

√(x + 14) = x - 2

By squaring on both sides

(x + 14) = (x - 2)^{2}

Using the algebraic identity

(a - b)^{2} = a^{2} + b^{2} - 2ab

(x + 14) = x^{2} + 4 - 4x

x^{2 }- 5x - 10 = 0

**The formula for the standard form of quadratic equation ax ^{2} + bx + c = 0 is written as**

x = [-b ± √(b^{2} - 4ac)] / 2a

**From the given equation we know that,**

a = 1, b = -5, c = -10

**Substituting it in the formula,**

x = [ -(-5) ± √{(-5)^{2} - 4(1)(-10)} ] / 2(1)

x = [ 5 ± √{25 + 40} ] / 2

**By further calculation,**

x = [5 ± √65] / 2

**Therefore, the values of x are (5 + √65)/2 and (5 - √65)/2.**

## Identify all of the following solutions of square root of x plus 14 end root plus 2 equals x.

**Summary:**

The solutions of square root of x plus 14 end root plus 2 equals x are (5 + √65)/2 and (5 - √65)/2.

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