Question

Find the roots 7x^2 + 46 = 32

Answer 1

i
`√(2)` (or no solution if you haven't learned about imaginary numbers yet)

Explanation:

The first thing you want to do is isolate x, or get x alone.

7x²+46=32

=> 7x²+46-46=32-46

=>7x²=-14

=>7x²÷7=-14÷7

=>x²=-2

If you have learned about imaginary numbers read on. If not, you have to realize that squaring any number can't result in a negative number. This means that there is no solution.

If you have learned about imaginary numbers, read on.

Now that you have x^2=-2, you can take the square root of both sides.

x=
`√(-2)`

Using a property about square roots (I don't know what it's called)

the equation becomes:

x=
`√(-1)√(2)`

And since
`√(-1)`=i, you can substitute in this value in to get x=i
`√(2)`.