solve the equation using square roots. x2 – 81 = 0
To solve the equation x^2 - 81 = 0 using square roots, you will take the square root of both sides and isolate x.
x^2 - 81 = 0
Take the square root of both sides:
√(x^2 - 81) = √0
Simplify:
√(x^2 - 81) = 0
On the left side, since we have a square root, it is necessary to consider both the positive and negative square roots of 0.
√(x^2 - 81) = ±√0
Simplify further:
√(x^2 - 81) = ±0
Now, solve for x.
Case 1: √(x^2 - 81) = 0
Simplifying, we have:
x^2 - 81 = 0
Adding 81 to both sides:
x^2 = 81
Taking the square root of both sides:
x = ±9
Case 2: √(x^2 - 81) = -0
Since -0 is equivalent to 0, we essentially have the same equation as in Case 1:
x^2 = 81
So, the solution for this equation is x = ±9.