Final answer:
The equation (w-4)²-49=0 is a difference of squares and can be factored to find the solutions w = -3 and w = 11.
Step-by-step explanation:
To solve the equation (w-4)²-49=0, you can use factoring of perfect squares. The given equation is a difference of squares which can be factored into (w-4+7)(w-4-7)=0. Setting each factor equal to zero gives us two potential solutions:
- w-4+7=0 → w=4-7 → w=-3
- w-4-7=0 → w=4+7 → w=11
Therefore, the solutions are w = -3 and w = 11.
Always remember to check the answer to ensure they satisfy the original equation.