Question

Can someone help me, please?

A quadratic equation is shown below:

x2 − 14x + 41 = 0

Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers?

Add 8 to both sides of the equation
Add 9 to both sides of the equation
Subtract 8 from both sides of the equation
Subtract 9 from both sides of the equation

Answer 1

Answer is A. Add 8 to both sides of the equation.

Answer 2

Can you explain it, if you don't mind?

Answer 3

Have you heard of the process of completing the square?

Answer 4

What you have to do is add half the coefficient of x squared to both sides to 'complete the square' and make it a perfect square.

Answer 5

So in your equation where 14 is the coefficient of x, half of 14 is 7, square it then you get 49. Since you already have 41 on the left hand side, you only need to add 8 to complete the square.

Answer 6

And then you have the equation in your form: (x-7)^2=8

Answer 7

Ohhh that makes so much sense, thank you so much! That helps a lot.