To complete the square for the equation [tex]\(x^2 + 8x = 4\)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
x^2 + 8x = 4
\][/tex]
2. The goal of completing the square is to transform the left-hand side of the equation into a perfect square trinomial. To do this, we need to add a specific value to both sides of the equation.
3. Look at the coefficient of the [tex]\(x\)[/tex] term, which is 8 in this case. Take half of this coefficient, which is [tex]\(\frac{8}{2} = 4\)[/tex].
4. Square this result:
[tex]\[
4^2 = 16
\][/tex]
5. Therefore, to complete the square, we need to add 16 to both sides of the equation.
So, the number that should be added to both sides of the equation [tex]\(x^2 + 8x = 4\)[/tex] to complete the square is [tex]\(16\)[/tex].
