Question

A quadratic equation is shown:

Answer 1

Answer:

The correct answer is the first option

Step-by-step explanation:

Quadratic Equation

The standard form of a quadratic equation is

$ax^2+bx+c=0$

Sometimes we need to change the expression of the same equation to the form

$(x-p)^2=q$

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

$x^2-14x+41=0$

Recall the square of a binomial is

$(x-p)^2=x^2-2px+p^2$

The first term is already present. The second term gives us the value of p:

$-2px=-14x$

Solving

$p=7$

Now we need to produce the third term $p^2=49$. We only have 41, thus we need to add 8 to both sides of the equation:

$x^2-14x+41+8=0+8$

The correct answer is the first option