Question

How do you solve `-2x^2 = -162`?

Answer 1

`x=+-9`

Explanation:

`color(blue)"Isolate " x^2" by dividing both sides by " -2`

`(cancel(-2) x^2)/cancel(-2)=(-162)/(-2)`

`rArrx^2=81`

`color(blue)"take the square root of both sides"`

`sqrt(x^2)=color(red)(+-)sqrt81`

`rArrx=color(red)(+-)9`

`["Note the " +-" solutions"]`

`color(blue)"As a check"`

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

`x=color(red)(+9)to-2xx(color(red)(+9))^2=-2xx81=-162`

`x=color(red)(-9)to-2xx(color(red)(-9))^2=-2xx81=-162`

`rArrx=+-9" are the solutions"`