Question

How do you solve `5x^2+64=0`?

Answer 1

This can be solved using the quadratic formula.

Explanation:

While there are many ways to solve quadratic equations like this one, the quadratic formula is one of the simplest.

The quadratic formula looks like this:
`x=(-b+-sqrt(b^2-4ac))/2a`

To use this equation, we simply plug in the values given in the problem. To find these values, we must acknowledge that a quadratic equation looks like this:
`y=ax^2+bx+c`

Once we know this, we can determine that our equation has an a value of 5, because it is multiplied by `x^2`. The b value must be zero, because none is given. If a number (x) is multiplied by zero, it will disappear. Finally, the c value must be 64, because it is not multiplied by any x value.
Now, we can plug in the values of a, b, and c.
`x=(-0+-sqrt(0^2-4(5)(64)))/(2(5))`

We simplify to get:
`x=(+-sqrt(-1280))/10`

The `+-` gives us two values for x. We solve for `+` and `-` separately. Because the value under the radical is negative, the answer will involve `i`, which is the variable given to the `sqrt(-1)`.
When we simplify, the two x values are:
`x=-(8sqrt(5)i)/5`
`x=(8sqrt(5)i)/5`