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 = a² + b² - 2ab

(x + 14) = x² + 4 - 4x

x² - 5x - 10 = 0

The formula for the standard form of quadratic equation ax² + bx + c = 0 is written as

x = [-b ± √(b² - 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.

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 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.