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=(-b\pm√(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=(-(-9)\pm√((-9)^2-4(2)(8)))/((2)(2)) \\ \\ x=(9\pm√(17))/(4) \end{gathered}`

Notice that you get two values:

`x_1=(9+√(17))/(4)`
`x_2=(9-√(17))/(4)`

Hence, the answer is:

`x=(9+√(17))/(4)\text{ or }x=(9-√(17))/(4)`