Question

The first few steps in solving the quadratic equation 8x2 + 80x = −5 by completing the square are shown.

8x2 + 80x = −5

8(x2 + 10x) = −5

8(x2 + 10x + 25) = −5 + ______

Which number is missing in the last step?

Answer 1

Missing number is 200.

Explanation:

In the completing the square method we follow the following steps,

Step 1 : Move constant term to the right side,

Step 2 : Make 1 as the coefficient of
`x^2`

Step 3 : Add square of the half of the coefficient of x in the left side and balance the equation,

Here, the given equation,

`8x^2+ 80x = -5`

`8(x^2 + 10x) = -5`

∵ coefficient of x = 10,

Half of 10 = 5,

Square of 5 = 25,

Thus, we need 25 inside the bracket in left side,

For this, add 200 on both side,

`8(x^2 + 10x+25) = -5+200`

Hence, missing number in the last step is 200.

Answer 2

200

Explanation:

8x^2 + 80x = −5

Factor out an 8

8(x^2 + 10x) = −5

Take the coefficient of the x term, divide by 2 and then square it

10/2 = 5, 5^2=25

Remember we have the 8 outside, so we are multiplying by 8

8*25 =200

Add 200 to each side

8(x^2 + 10x + 25) = −5 + 200