(5m+1)^2=7

Answer 1

To solve the equation \( (5m + 1)^2 = 7 \), we will first take the square root of both sides.

1. Take the square root: \[ 5m + 1 = \pm \sqrt{7} \]

2. Now we have two cases to consider:

   • Case 1: \( 5m + 1 = \sqrt{7} \)
   • Case 2: \( 5m + 1 = -\sqrt{7} \)

Case 1:

\[ 5m + 1 = \sqrt{7} \]

Subtract 1 from both sides: \[ 5m = \sqrt{7} - 1 \]

Now, divide by 5: \[ m = \frac{\sqrt{7} - 1}{5} \]

Case 2:

\[ 5m + 1 = -\sqrt{7} \]

Subtract 1 from both sides: \[ 5m = -\sqrt{7} - 1 \]

Now, divide by 5: \[ m = \frac{-\sqrt{7} - 1}{5} \]

Final Solutions:

Thus, the solutions for \( m \) are: \[ m = \frac{\sqrt{7} - 1}{5} \quad \text{and} \quad m = \frac{-\sqrt{7} - 1}{5} \]