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

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

Then x is:

$\begin{gathered} x=\frac{24-12}{4}=\frac{12}{4}=3 \\ or \\ x=\frac{24+12}{4}=\frac{36}{4}=9 \end{gathered}$