Final answer:
To solve the equation -5x^2 - 20x + 35 = 30 using completing the square, we can rewrite it as -5(x^2 + 4x) = -5. Next, we complete the square by adding and subtracting half the coefficient of x, squared. The solutions to the equation are x = -3 and x = -1.
Step-by-step explanation:
To solve the equation -5x2 - 20x + 35 = 30 using completing the square, we can rewrite it as -5(x2 + 4x) = -5. Next, we complete the square by adding and subtracting half the coefficient of x, squared. In this case, that would be 22 = 4. So, we have -5(x2 + 4x + 4 - 4) = -5. Simplifying further, we get -5((x + 2)2 - 4) = -5.
Dividing both sides by -5, we have ((x + 2)2 - 4) = 1. Solving for x, we take the square root of both sides to get x + 2 = ±√1. Thus, x + 2 = -1 or x + 2 = 1. Solving for x, we have x = -1 - 2 or x = 1 - 2.
Therefore, the solutions to the equation -5x2 - 20x + 35 = 30 are x = -3 and x = -1.