(x/4)²=9
taking square root ... x/4 = ± 3
dividing by 4 ... x = ± 3/4
thats not right its 12 or -12
To solve the equation (x/4)² = 9, we can use the concept of square roots and simplification.
Step 1: Recognize that the given equation is in the form of (a/b)² = c, where a represents x, b represents 4, and c represents 9.
Step 2: Take the square root of both sides of the equation. By applying the square root, the exponent of 2 is "undone" or cancelled out.
√((x/4)²) = √9
Step 3: Simplify the equation further. The square root of a square term results in the absolute value of the term itself:
|x/4| = 3
Step 4: Remove the absolute value by considering both positive and negative solutions:
x/4 = 3 or x/4 = -3
Step 5: Solve for x in each equation:
For the first equation, x/4 = 3:
Multiply both sides of the equation by 4 to isolate x:
x = 12
For the second equation, x/4 = -3:
Multiply both sides of the equation by 4 to isolate x:
x = -12
Therefore, the solutions to the equation (x/4)² = 9 are x = 12 and x = -12.