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
