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

Question

asked Oct 5, 2022 92.4k views

1 Answer

Wesgarrison · Answer 1 · 2022-10-09T09:56:46+0000

Answer:

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

Explanation:

Let
$√(-4-5\cdot x) = x$ , we solve for
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.