Question

What constant $c$ makes the expression a perfect square? \[49x^2-42x c\]

Answer 1

Explanation:

`49x^2-42x+((42)/(2))^2=49x^2-42x+((42)/(2) )^2` (completing the square)

`49x^2-42x+441=49x^2-42x+21^2`

`=(7x-21)^2`

So
`49x^2-42x+441=(7x-21)^2`

Solution: The required constant is 441.

Remember: Completing the square IN
`ax^2+bx+c` involves adding
`((b)/(2) )^2` to both sides of the equation. THIS KEEPS IT BALANCED AND ALLOWS US TO MAKE A PERFECT SQUARE.