Given parameters:
Equation:
(x-4)²=9
Problem: Solve the equation by both factoring and extracting the square root.
Solution:
Starting equation:
(x-4)²=9
Subtracting 9 from both sides brings us to zero;
(x-4)² - 9 = 0
(x -4)² - 3² = 0
This fits the concept of the difference of squares;
x² - y² = (x + y)(x-y)
Let x = x-4 and y = -3
Then input and solve;
(x - 4 -3)(x - 4 -(-3)) = 0
(x - 7)(x - 1) = 0
S thus,
x - 7 = 0 or x-1 = 0
x = 7 or 1
<pBy extracting the square roots;
(x-4)² = 9
√(x-4)² = √9
x - 4 = 3
x = 4 + 3 = 7; however, this is not the sole solution
Thus, direct extraction of the square root is not the method for complete solutions.
