Question

Solve by taking the square root. 25(x-1)²-64=0 x

Answer 1

The equation 25(x-1)²-64=0 is solved by isolating the squared term, taking the square root of both sides, and solving for x, which results in the solutions x = 13/5 and x = -3/5.

Step-by-step explanation:

To solve the equation 25(x-1)²-64=0 by taking the square root, first add 64 to both sides to isolate the squared term:

• 25(x-1)² = 64

Next, divide both sides by 25:

• (x-1)² = √(64/25)

Now take the square root of both sides, remembering to consider both the positive and negative square roots:

• x-1 = ±√(64/25)
• x-1 = ±(8/5)

Add 1 to both sides to solve for x:

• x = 1 ± 8/5
• x = 1 + 8/5 = 13/5 or x = 1 - 8/5 = -3/5

Thus, the solutions are x = 13/5 and x = -3/5.