Question

Solve: 9x 2+ 2x = –3 using the quadratic formula. step by step please to understand better

Answer 1

Step-by-step explanation: To solve the following equation

`9x^2+2x=-3`

We can use the following quadratic formula

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

Step 1: Let's compare our equation with a generic quadratic equation as follows

As we can see above, first we move -3 from the second term to the first term and when we do that we change its sign to +3. Now we know that a = +9, b = +2 and c = +3.

Step 2: Now all we need to do is to substitute the values of a, b and c into our quadratic formula and solve it to find the roots as follows

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-2\pm\sqrt[]{2^2-4\cdot9\cdot3}}{2\cdot9} \\ x=\frac{-2\pm\sqrt[]{4^{}-108}}{18} \\ x=\frac{-2\pm\sqrt[]{-104}}{18} \\ x=\frac{-2\pm\sqrt[]{-104}}{18} \end{gathered}`

Final answer: As we can see above inside the square root there is a negative number -104 which means this quadratic equation has no real solutions.