Question

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

Answer 1

Solution:

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

$y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case,

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

By substituting into the quadratic formula, we have

$\begin{gathered} y=\frac{-(-9)\pm\sqrt{(-9)^2-(4\times-6\times1)}}{2(-6)} \\ =\frac{9\pm\sqrt{81+24}}{-12} \\ =\frac{9\pm\sqrt{105}}{-12} \\ This\text{ implies that} \\ y=\frac{9+\sqrt{105}}{-12}\text{ or y=}\frac{9-\sqrt{105}}{-12} \\ thus, \\ y=0.10391\text{ or y=-1.60391} \\ \Rightarrow y\approx0.10\text{ or -1.60 \lparen nearest hundredth\rparen} \end{gathered}$

Hence, the solution to the above equation is

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