Question

Solve for v, where v is a real √-v+6=v

number. (If there is more than one solution, separate them with commas.)

Answer 1

To solve the equation √-v+6=v, subtract 6 from both sides, square both sides, rearrange the equation, factor the quadratic equation, and solve for v.

Step-by-step explanation:

To solve for v in the equation √-v+6=v, we need to isolate v on one side of the equation. Here are the steps to solve:

1. Start by subtracting 6 from both sides of the equation: √-v = v - 6
2. To remove the square root, square both sides of the equation: (-v) = (v - 6)^2
3. Expand the right side of the equation: -v = v^2 - 12v + 36
4. Rearrange the equation to isolate v on one side: v^2 - 11v + 36 = 0
5. Factor the quadratic equation: (v - 4)(v - 9) = 0
6. Solve for v by setting each factor equal to 0: v - 4 = 0 or v - 9 = 0
7. Finally, solve for v: v = 4 or v = 9