Question

Please help!! I’m stuck on this

√-4 - 5x = x

A. x = -1 or x = 4

B. x = -1 or x = -4

C. x = 1 or x = -4

D. x = -5 or x = 4/5

E. x = 1 or x = 4

Answer 1

B.
`x = -4\,\lor \,x = -1`

Explanation:

Let
`√(-4-5\cdot x) = x`, we solve for
`x` by algebraic means.

1)
`√(-4-5\cdot x) = x` Given

2)
`-4-5\cdot x = x^(2)` Definition of power/Symmetry of equality

3)
`x^(2)+5\cdot x + 4 = 0` Compatibility with addition/Commutative and associative properties/Existence of additive inverse/Modulative property

4)
`(x+4)\cdot (x+1) = 0`
`x^(2)+(a+b)\cdot x +a\cdot b = (x + a)\cdot (x+b)`

5)
`x = -4\,\lor \,x = -1` Result

Hence, the correct answer is B.