Question

Solve 2x^2+x-4=0x^2+1/2x+___=2+____

Answer 1

We have the following expression:

`2x^2+x-4=0`

By dividing both sides by 2, we get

`x^2+(1)/(2)x-2=0`

At this point we can apply the quadratic formula:

`\begin{gathered} \text{For ax}^2+bx+c=0 \\ x\text{ is given by} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}`

where a is 1, b is 1/2 and c is -2. By substituting these values, we get

`x=\frac{-(1)/(2)\pm\sqrt[]{((1)/(2))^2-4(1)(-2)}}{2}`

which gives

`\begin{gathered} x=\frac{-(1)/(2)\pm\sqrt[]{(1)/(4)+8}}{2} \\ x=\frac{-(1)/(2)\pm\sqrt[]{(33)/(4)}}{2} \\ x=\frac{-(1)/(2)\pm\frac{\sqrt[]{33}}{2}}{2} \\ x=-(1)/(4)\pm\frac{\sqrt[]{33}}{4} \end{gathered}`

Then, the solutions are

`\begin{gathered} x=\frac{-1+\sqrt[]{33}}{4} \\ \text{and} \\ x=\frac{-1-\sqrt[]{33}}{4} \end{gathered}`