Question

What substitution should be used to rewrite 6(x + 5)2 + 5(x + 5) – 4 = 0 as a quadratic equation?

Answer 1

how about: y = (x + 5)

6y^2 + 5y - 4 = 0

(2y - 1)(3y + 4) = 0

2y - 1 = 0
y = 1/2

3y + 4 = 0
y = -3/4

replace substitution, y = (x + 5)

1/2 = (x + 5)
-9/2 = x

-3/4 = (x + 5)
-23/4 = x

Answer 2

we have

`6(x+5)^(2)+5(x+5)-4=0`

we know that

The equation of a quadratic equation is of the form

`ax^(2) +bx+c=0`

so

Let

`u=(x+5)`

Substitute

`6(u)^(2)+5(u)-4=0`

therefore

the answer is

The substitution should be
`u=(x+5)`