Question

EASY MATH

WILL GIVE BRAINLIEST.

Solve the equation using inverse operations. Check your solutions. In you final answer, include all of your work.


-x^2= -36


I need to find both of the answers: Positive and Negative

Please provide the steps!

Answer 1

Answer:

Step-by-step explanation:

First of all, $-x^2$ is the same thing as $-1x^2$.  The -1 is "stuck" to the x-squared term by multiplication.  The inverse of multiplication is division.  So we are going to "undo" that multiplication by dividing both sides of the equation by a -1:

$\frac{-1x^2}{-1}=\frac{-36}{-1}$

A negative divided by a negative gives us a positive, so the equation now is

$x^2=36$

This is a second degree polynomial since the power on the x is a 2.  That means that we will have 2 answers for what x is equal to.  The inverse of squaring is taking the square root.  What you take the square root (or any even root) of a number, you get both the positive (the principle) root and the negative.  Think of it like this, 3 * 3 = 9 so the square root of 9 is 3.  BUT

-3 * -3 = 9 also, so the square root of 9 is also -3.  We have both the positive and negative roots to consider.  That means that if we take the square root of 36, we have both the positive and the negative root to consider.  The square root of 36 on your calculator will give you only the positive root, 6, but we have to take both the positive and the negative so the 2 answers are 6 and -6