Question

Question 10 Multiple Choice Worth 5 points)

(09.02 LC)
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 = 9, 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

Add 8 to both sides of the equation

Explanation:

We have been given the quadratic equation;

x^2 - 14x +41 = 0

we are required to complete the square in order to express it in the form;

(x - p)^2 = q

In order to do this we need to find a constant c, such that;

`c=((b)/(2))^(2)`

where b is the coefficient of x in the quadratic equation. In our case b = -14. Therefore,

`c=((-14)/(2))^(2)=49`

Therefore, for us to complete the square, the left hand side of the quadratic equation should be;

x^2 - 14x +49

Since we already have 41, we can simply add 8 to make it 49. Thus, the first correct step to write the above equation in the form (x - p)2 = 9, where p and q are integers is to Add 8 to both sides of the equation