How do you find the value of c that makes #x^2+17x+c# into a perfect square?
c = 72.25
in complete the square, we should add square of ½ of the coefficient of x to constant term.
Here 17 is the coefficient of x, ½ of 17 is 8.5 and its square is 72.25
Use the pattern
Set the middle term of the pattern equal to middle term of the given equation and then solve for c.
Set the middle term of the pattern equal to middle term of the given equation:
The first step in solving for c is to divide both sides of the equation by 2x:
The next step in solving for c is to square both sides:
This is how you find the value of c that makes the quadratic a perfect square.
Some additional information:
If the middle term of the given equation is negative, then use the pattern
Let's do an example, given
Set the middle terms equal:
Divide both sides by -2x:
Square both sides:
I hope that this helps.