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

2 Answers
Jini A.
Jan 25, 2017

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

Douglas K.
Jan 25, 2017

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.

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