Question

Solve for x. Enter the solutions from least to greatest.2x^2 - 24x + 54 = 0lesser x =greater x =

Answer 1

To solve the equation

`2x^2-24x+54=0`

we are going to use the general formula for quadratic equations:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

In our case a=2, b=-24 and c=54. Then

`\begin{gathered} x=\frac{-(-24)\pm\sqrt[]{(-24)^2-4(2)(54)}}{2(2)} \\ =\frac{24\pm\sqrt[]{576-432}}{4} \\ =\frac{24\pm\sqrt[]{144}}{4} \\ =(24\pm12)/(4) \end{gathered}`

Then x is:

`\begin{gathered} x=(24-12)/(4)=(12)/(4)=3 \\ or \\ x=(24+12)/(4)=(36)/(4)=9 \end{gathered}`