Question

If using the method of completing the square to solve the quadratic equation

x² + 7x-4 = 0, which number would have to be added to "complete the square"?

Answer 1

See below

Explanation:

x^2 + 7x - 4 = 0 take 1/2 of the 'x ' coefficient (this is 7/2) and do this:

(x + 7/2)^2 -4 now when you expand this (see botom line) you will see you have added 49/4 to the equation....you will need to subtract this for the equation to be the same :

(x+7/2)^2 - 49/4 - 4 = 0 then simplify to:

(x+7/2)^2 - 65/4 = 0 you can re-arrange if needed to this:

(x+7/2)^2 = 65/4

(x+7/2)^2 = x^2 + 7x + 49/4 <====== this needs to be subtracted

Answer 2

The number 49/4 should be added on both sides of
`x^2 + 7x = 4` to complete the square.

Explanation:

`x^(2) + 7x +(49)/(4) = 4 + (49)/(4)`

`{4x^(2) + 28x + (49)/(4) = {16 + (49)/(4)`

`{4x^(2) + 28x + 49} = 16 + 49`

`(2x + 7)2 = 65` [since
`a^(2) + 2ab + b^(2) = (a + b)^(2)`]

`(2x + 7)^(2)`
`=`
`(\sqrt65)^2`