Question

Solve by taking the square roots: 9(x−1)²−16=0. Use the key / to write fractions if necessary. x= x=?

Answer 1

To solve the equation 9(x-1)²-16=0, isolate the square term and take the square root, giving two solutions for x: 7/3 and -1/3.

Step-by-step explanation:

To solve the equation 9(x−1)²−16=0, we first want to isolate the squared term. Here are the steps for solving:

1. Add 16 to both sides to get 9(x−1)² = 16.
2. Divide both sides by 9 to get (x−1)² = 16/9.
3. Take the square root of both sides to get x−1 = ±√(16/9).
4. Since √(16/9) is the square root of a fraction, we find that it is ± 4/3.
5. Next, we solve for x by adding 1 to both sides, resulting in two solutions: x = 1 + 4/3 and x = 1 - 4/3.
6. Simplifying these, we get the two solutions for x: x = 7/3 and x = -1/3.