Solve for x
Question 1 of 3
Solution:
Step 1: Recognize difference of squares
\[x^2 - 64 = 0\]
This is a difference of two squares: \(x^2 - 8^2\)
\[(x - 8)(x + 8) = 0\]
Step 2: Solve for x
Either \(x - 8 = 0\) or \(x + 8 = 0\)
\[x_1 = 8 \quad \text{or} \quad x_2 = -8\]
Solution:
Step 1: Rearrange to standard form
\[x^2 = 81\]
\[x^2 - 81 = 0\]
Step 2: Recognize difference of squares
This is a difference of two squares: \(x^2 - 9^2\)
\[(x - 9)(x + 9) = 0\]
Step 3: Solve for x
Either \(x - 9 = 0\) or \(x + 9 = 0\)
\[x_1 = 9 \quad \text{or} \quad x_2 = -9\]
Solution:
Step 1: Factor out common factor
\[2x^2 - 50 = 0\]
\[2(x^2 - 25) = 0\]
Step 2: Recognize difference of squares
\(x^2 - 25\) is a difference of two squares: \(x^2 - 5^2\)
\[2(x - 5)(x + 5) = 0\]
Step 3: Solve for x
Either \(x - 5 = 0\) or \(x + 5 = 0\)
\[x_1 = 5 \quad \text{or} \quad x_2 = -5\]
