Question

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

Answer 1

5(x^2+8x)=14
5(x^2+8x+16)=5(x^2+8x)+5*16=5(x^2+8x)+80=14+80=94
The corect answer is the second

Answer 2

we have

`5x^(2) +27x=14-13x`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`5x^(2) +27x+13x=14`

`5x^(2) +40x=14`

Factor the leading coefficient

`5(x^(2) +8x)=14`

Complete the square. Remember to balance the equation by adding the same constants to each side.

`5(x^(2) +8x+4^(2))=14+5(4^(2))`

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

`5(x^(2) +8x+16)=94`

therefore

the answer is the option

`5(x^(2) +8x+16)=94`