Question

Solve: 9x 2+ 2x = –3 using the quadratic formula.

Answer 1

x = (-1 + √(26)i)/9

x = (-1 - √(26)i)/9

Step-by-step explanation:

If we have an equation of the form ax² + bx + c = 0, we can solve it using the quadratic equation

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

In this case, the given equation is

9x² + 2x = -3

This can be rewritten as

9x² + 2x + 3 = -3 + 3

9x² + 2x + 3 = 0

So, a = 9, b = 2 and c = 3. Therefore, the solutions using the quadratic equation are

`\begin{gathered} x=\frac{-2\pm\sqrt[]{2^2-4(9)(3)}}{2(9)} \\ x=\frac{-2\pm\sqrt[]{-104}_{}}{18} \\ x=\frac{-2\pm\sqrt[]{104}i}{18} \\ x=\frac{-2\pm2\sqrt[]{26}i}{18} \\ \text{Then} \\ x=\frac{-2+2\sqrt[]{26}i}{18}=\frac{-1+\sqrt[]{26}i}{9} \\ or \\ x=\frac{-2-2\sqrt[]{26}i}{18}=\frac{-1-\sqrt[]{26}i}{9} \end{gathered}`

therefore, the solutions are

x = (-1 + √(26)i)/9

x = (-1 - √(26)i)/9