Question

-5x^2+9=0 solve quadratic equation

Answer 1

We are asked to solve the following quadratic equation:

$-5x^2+9=0$

To do that, we will solve for "x", first by subtracting 9 on both sides, like this:

$\begin{gathered} -5x^2+9-9=-9 \\ -5x^2=-9 \end{gathered}$

Now we will divide both sides by -5, like this:

$-\frac{5x^2}{-5}=-\frac{9}{-5}$

Solving the operations, we get:

$x^2=\frac{9}{5}$

Now we take the square root on both sides of the equation, like this:

$\sqrt[]{x^2}=\sqrt[]{\frac{9}{5}}$

Solving the operations:

$\begin{gathered} x=\sqrt[]{\frac{9}{5}} \\ x=\pm\frac{3}{\sqrt[]{5}} \end{gathered}$

Since the square root has positive and negative solutions, the equation has two possible solutions, these are:

$\begin{gathered} x=\frac{3}{\sqrt[]{5}}\text{ and} \\ x=-\frac{3}{\sqrt[]{5}} \end{gathered}$