Question

How do you solve `-19 = 30 - 7x^2`?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(red)(30)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`- color(red)(30) - 19 = - color(red)(30) + 30 - 7x^2`

`-49 = 0 - 7x^2`

`-49 = -7x^2`

Next, divide each side of the equation by `color(red)(-7)` to solve for `x^2` while keeping the equation balanced:

`(-49)/color(red)(-7) = (-7x^2)/color(red)(-7)`

`7 = (color(red)(cancel(color(black)(-7)))x^2)/cancel(color(red)(-7))`

`7 = x^2`

`x^2 = 7`

Now, take the square root of each side of the equation to solve for `x` while keeping the equation balanced. Remember, the square root of the number yields both a positive and a negative result:

`sqrt(x^2) = +-sqrt(7)`

`x = +-sqrt(7) = 2.646` rounded to the nearest thousandth.