Question

How do you solve 2(x-3)^2 + 5 = 29 using square roots and SADMEP?

A) Expand and simplify the equation, isolate x, and solve.
B) Apply the square root to both sides and solve for x.
C) Use SADMEP: Subtraction, Addition, Division, Multiplication, Exponents, and Parentheses.
D) Factor the quadratic and apply the square root to solve for x.

Answer 1

The correct way to solve the equation 2(x-3)^2 + 5 = 29 using square roots is to first isolate the squared term, then apply the square root to both sides, considering both the positive and negative roots, and finally solve for the variable x.

Step-by-step explanation:

To solve the equation 2(x-3)^2 + 5 = 29 using square roots, you should follow these steps:

1. First, subtract 5 from both sides to isolate the term containing the variable. This leaves you with 2(x-3)^2 = 24.
2. Divide both sides by 2 to simplify. The equation now reads (x-3)^2 = 12.
3. Apply the square root to both sides. Remember that when you take the square root, you must consider both the positive and negative roots. So, x - 3 = ±√12.
4. Add 3 to both sides to solve for x. Thus, x = 3 ± √12.

Therefore, the correct approach would be option B: Apply the square root to both sides and solve for x.