how many solutions are in the solution set for 2(x−5)2+2=20 .

Answer 1

To solve the equation \( 2(x - 5)^2 + 2 = 20 \), we start by isolating the squared term.

1. Subtract 2 from both sides: \[ 2(x - 5)^2 = 18 \]

2. Divide both sides by 2: \[ (x - 5)^2 = 9 \]

3. Now, take the square root of both sides: \[ x - 5 = 3 \quad \text{or} \quad x - 5 = -3 \]

4. Solve each equation:

   • For \( x - 5 = 3 \): \[ x = 3 + 5 = 8 \]
   • For \( x - 5 = -3 \): \[ x = -3 + 5 = 2 \]

Thus, the solutions are \( x = 8 \) and \( x = 2 \).

In conclusion, there are 2 solutions in the solution set for the equation \( 2(x - 5)^2 + 2 = 20 \).