Question

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.−6y^2 − 9y = −1

Answer 1

Given the equation below:

`-6y^2-9y=-1`

The above equation can also be expressed as

`-6y^2-9y+1=0`

To solve using the quadratic formula for the above equation expressed as

`y=(-b\pm√(b^2-4ac))/(2a)`

In this case,

`\begin{gathered} a=-6 \\ b=-9 \\ c=1 \end{gathered}`

By substituting into the quadratic formula, we have

`\begin{gathered} y=(-(-9)\pm√((-9)^2-(4*-6*1)))/(2(-6)) \\ =(9\pm√(81+24))/(-12) \\ =(9\pm√(105))/(-12) \\ This\text{ implies that} \\ y=(9+√(105))/(-12)\text{ or y=}(9-√(105))/(-12) \\ thus, \\ y=0.10391\text{ or y=-1.60391} \\ \Rightarrow y\approx0.10\text{ or -1.60 \lparen nearest hundredth\rparen} \end{gathered}`

Hence, the solution to the above equation is

`y=0.10\text{ or y = -1.60}`