The first few steps in solving the quadratic equation 5x2 + 27x = 14 - 13x by completing the square are shown.

5x2 + 27x = 14 - 13x

5x2 + 40x = 14

5 (x2 + 8x) = 14

Which is the best step to do next to solve the equation by completing the square?

5 (x2 + 8x + 16) = 30

5 (x2 + 8x + 16) = 94

5 (x2 + 8x + 4) = 18

5 (x2 + 8x + 4) = 34

The second option is the best step to do next in solving this equation. In this equation, a = 1, b = 8 and c is unknown. To solve for c, divide b by 2 and square it. (Mind the signs!) So 8/2 = 4, then 4² = 16. Because we added 16 to the left hand side of the equation, we add the same to the right hand side. But since the whole equation on the left is multiplied by 5, we add 16*5 to the other side, not 16. 16*5 equals 80, and 80 + 14 = 94.

The correct answer among the choices given is option 2.

Completing the square is done as follows:

1. Write the equation in a way that the constants are in the right side while the terms with x are on the left.

5x^2 + 27x + 13x = 14

5x^2 + 40x = 14

2. Make sure that the coefficient of the x^2 term is 1.

5 (x^2 + 8x) = 14

3. Adding a term to both sides that will complete the square in the left side. This is done by dividing the coefficient of the x term by 2 and squaring it. Note: The same amount should be added to the right side to balance the equation.

5 (x^2 + 8x + 16) = 14 + 80

5 (x+4) ^2 = 94