Answer:
The correct answer is the first option
Step-by-step explanation:
Quadratic Equation
The standard form of a quadratic equation is
[tex]ax^2+bx+c=0[/tex]
Sometimes we need to change the expression of the same equation to the form
[tex](x-p)^2=q[/tex]
To accomplish that change, we usually modify the left-hand expression to make it look like the square of a binomial.
The given quadratic equation is
[tex]x^2-14x+41=0[/tex]
Recall the square of a binomial is
[tex](x-p)^2=x^2-2px+p^2[/tex]
The first term is already present. The second term gives us the value of p:
[tex]-2px=-14x[/tex]
Solving
[tex]p=7[/tex]
Now we need to produce the third term [tex]p^2=49[/tex]. We only have 41, thus we need to add 8 to both sides of the equation:
[tex]x^2-14x+41+8=0+8[/tex]
The correct answer is the first option
