How do you find the value of c that makes #x^2+17x+c# into a perfect square?
2 Answers
c = 72.25
Explanation:
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
Consider
Use the pattern
Set the middle term of the pattern equal to middle term of the given equation and then solve for c.
Explanation:
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.