Question

quadratic square root
$x^2 - 64 = 0$
solutions ?

Explanation:

Step1: Isolate the squared term

We start with the equation \( x^2 - 64 = 0 \). To isolate \( x^2 \), we add 64 to both sides of the equation. This gives us \( x^2 = 64 \).

Step2: Take the square root of both sides

Now that we have \( x^2 = 64 \), we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution because \( (\pm a)^2 = a^2 \). So, \( x = \pm\sqrt{64} \).

Step3: Calculate the square root

We know that \( \sqrt{64} = 8 \), so substituting that in, we get \( x = \pm 8 \).

Answer:

The solutions to the equation \( x^2 - 64 = 0 \) are \( x = 8 \) and \( x = -8 \).