Solve for x. Provide an explanation, please.
-X^2+36=0
x^2=36
take the square root of each side.
x= +-6
Thank you.
To solve for x in the equation -x^2 + 36 = 0, we need to isolate the variable x.
Step 1: Move the constant term to the other side of the equation.
To do this, subtract 36 from both sides:
-x^2 + 36 - 36 = 0 - 36
This simplifies to:
-x^2 = -36
Step 2: Divide both sides of the equation by -1 to make the coefficient of x^2 positive.
Dividing by a negative number flips the inequality sign, so we have:
(-x^2) / (-1) = (-36) / (-1)
x^2 = 36
Step 3: Take the square root of both sides.
Since x^2 = 36, taking the square root on both sides gives us two possible solutions:
x = √36 or x = -√36
Step 4: Simplify the square root.
The square root of 36 is 6, so we have:
x = 6 or x = -6
Therefore, the solutions to the equation -x^2 + 36 = 0 are x = 6 and x = -6.