Question

Complete the square to transform the quadratic equation into the form (x – p)2 = q. x2 4x - 19 = 5

Answer 1

The answer is (x+2)^2 - 28

Work:

x^2 + 4x - 19 = 5
x^2 + 4x - 24
(x^2 + 4x ) - 24
(x^2 + 4x + 4) -24 - 4
(x^2 + 4x + 4) - 28
(x + 2) -28

Answer 2

(x - 2)^2 = 28

Explanation:

The given equation is x^2 - 4x - 19 = 5

We have to convert this in (x - p)^2 = q form.

x^2 - 4x - 19 = 5

Here b = 4, find b/2 and make it square.

-4/2 = -2, the square of -2 is 4.

Now add 4 on both sides, we get

(x^2 - 4x + 4 ) -19 = 5 + 4

(x^2 - 4x + 4) -19 = 9

(x^2 - 4x + 4) = 9 +19

(x - 2)^2 = 28

Now we have the equation in the form of (x - p)^2 = q

Hope this will helpful.

Thank you.