Complete the square to identify the two values that solve the following quadratic equation: x2−16x−13=4.(1 point)

Answer 1

To solve the quadratic equation $x^2-16x-13=4$ by completing the square, we first rearrange the equation:

$$x^2-16x-13-4=0$$

This simplifies to:

$$x^2-16x-17=0$$

Next, we will complete the square for the expression $x^2-16x$. To do this, we take the coefficient of $x$, which is $-16$, divide it by 2 to get $-8$, and then square it to get $64$.

Now, we add and subtract $64$ inside the equation:

$$x^2-16x+64-64-17=0$$

This simplifies to:

$$(x-8{)}^2-81=0$$

Next, we isolate the square:

$$(x-8{)}^2=81$$

Now, we'll take the square root of both sides:

$$x-8=9\text{or}x-8=-9$$

Solving for $x$ in each case gives:

1. $x-8=9$ leads to $x=17$.
2. $x-8=-9$ leads to $x=-1$.

Thus, the two values that solve the quadratic equation $x^2-16x-13=4$ are:

$$\boxed{{\displaystyle 17\text{ and }-1}}$$