How do you find the value of c that makes #x^2+17x+c# into a perfect square?

2 Answers
Jan 25, 2017

Answer:

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
#(a+b)^2 = a^2+2ab+b^2#

#(x+8.5)^2 = x^2 + 2 (8.5x) + (8.5)^2 = x^2 + 17x + 72.25#

Jan 25, 2017

Answer:

Use the pattern #(x + sqrtc)^2 = x^2 + 2(sqrtc)x + c#
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:

#2(sqrtc)x = 17x#

The first step in solving for c is to divide both sides of the equation by 2x:

#sqrtc = 17/2#

The next step in solving for c is to square both sides:

#c = 289/4#

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 #(x - sqrtc)^2 = x^2 - 2(sqrtc)x + c#

Let's do an example, given #x^2 - 8x + c#

Set the middle terms equal:

#-2(sqrtc)x = -8x#

Divide both sides by -2x:

#(sqrtc) = 4#

Square both sides:

#c = 16#

I hope that this helps.