Question

Use the quadratic formula to solve for X 5x^2 +2x=2

Answer 1

Given:

`5x^2+2x=2`

To solve for x using the quadratic formula, we simplify the given equation first:

`\begin{gathered} 5x^2+2x=2 \\ 5x^2+2x-2=0 \end{gathered}`

Next, we use the quadratic formula of the form ax^2+bx+c=0:

`x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

where:

a=5

b=2

c=-2

We plug in what we know:

`\begin{gathered} x_(1,2)=\frac{-2\pm\sqrt[]{2^2^{}-4(5)(-2)}}{2(5)} \\ \text{Simplify} \\ x_(1,2)=\frac{-2\pm\sqrt[]{44}}{10} \\ x_(1,2)=\frac{-2\pm2\sqrt[]{11}}{10} \end{gathered}`

We separate the solutions:

`x_1=\frac{-2+2\sqrt[]{11}}{10}=\frac{-1+\sqrt[]{11}}{5}=0.46`
`x_2=\frac{-2-2\sqrt[]{11}}{10}=-\frac{1+\sqrt[]{11}}{5}=-0.86`

Therefore,

`x=0.46,-0.86`