Question

How can i solve by completing the square 4r^2-28r=-49

Answer 1

To complete the square, the second degree term must have a coefficient of 1.
Since the second degree term here has a coefficient of 4, we start by dividing each term on both sides by 4.


`4r^2 - 28r = -49`


`(4r^2)/(4) - (28)/(4)r = -(49)/(4)`


`r^2 - 7r = -(49)/(4)`

Now we can complete the square.
First, we need to find what number completes the square.
We take the coefficient of the first degree term, -7 in this case.
Divide it by 2 and square it. -7 divided by 2 is the fraction -7/2.
Now we square -7/2 to get 49/4.
We add 49/4 to both sides.


`r^2 - 7r + (49)/(4) = -(49)/(4) + (49)/(4)`


`(r - (7)/(2))^2 = 0`


`r - (7)/(2) = 0`


`r = (7)/(2)`