Question

Solve by completing the square:

Answer 1

Answer:

d. x = -5 or 1

Step-by-step explanation:

x² + 4x - 5 = 0

completing the square means that we find an expression in the form

(x + a)(x+a) = (x+a)²

or

(x - a)(x - a) = (x - a)²

the fact that the middle term is +4x tells us we are looking for

(x + a)²

so,

(x + a)² = x² + 2ax + a²

now let's compare this with what we have :

x² = x²

2ax = 4x

2a = 4

a = 2

that means the full square is

(x + 2)² = x² + 4x + 4

but we have -5 in our original equation.

what do we need to do to change this to +4 ?

we have to add 9.

and to keep the equation true, we need to do this on both sides :

x² + 4x -5 + 9 = 0 + 9

x² + 4x + 4 = 9

(x + 2)² = 9

x + 2 = ±3

x + 2 = +3

x = 1

x + 2 = -3

x = -5

and that gives us answer option d. -5 or 1