Question

Please help me with this problem:Use the quadratic formula.2x^2 − 9x + 8 = 0 Enter the solutions, in simplified radical form, in the boxes.x = __ or x = __

Answer 1

Given the Quadratic Equation:

$2x^2-9x+8=0$

You need to use the Quadratic Formula in order to solve it:

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

Notice that the equation is written in this form:

$ax^2+bx+c=0$

Then, in this case:

$\begin{gathered} a=2 \\ b=-9 \\ c=8 \end{gathered}$

Now you can substitute values into the formula and evaluate:

$\begin{gathered} x=\frac{-(-9)\pm\sqrt{(-9)^2-4(2)(8)}}{(2)(2)} \\ \\ x=\frac{9\pm\sqrt{17}}{4} \end{gathered}$

Notice that you get two values:

$x_1=\frac{9+\sqrt{17}}{4}$$x_2=\frac{9-\sqrt{17}}{4}$

Hence, the answer is:

$x=\frac{9+\sqrt{17}}{4}\text{ or }x=\frac{9-\sqrt{17}}{4}$