Final answer:
To solve the equation, we expand (V+5)², subtract it from both sides, factor the resulting quadratic, and solve for V, yielding the solutions V = 1 and V = 5.
Step-by-step explanation:
To solve the equation 2V² + 4V + 30 = (V+5)², we start by expanding the right side of the equation. The squared term (V+5)² can be expanded to V² + 10V + 25. Then, we subtract the expanded form from both sides to get all terms on one side and set the equation to zero:
2V² + 4V + 30 = V² + 10V + 25
2V² + 4V + 30 - (V² + 10V + 25) = 0
V² - 6V + 5 = 0
Next, we factor the resulting quadratic equation. Since 1 * 5 = 5 and 1 + 5 = 6, the factors of the quadratic equation are (V - 1)(V - 5) = 0. Finally, we can set each factor to zero and solve for V:
V - 1 = 0 or V - 5 = 0
V = 1 or V = 5
So, the solutions to the original equation are V = 1 and V = 5.