Answered

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What number should be added to both sides of the equation to complete the square?

[tex]\[ x^2 + 8x = 4 \][/tex]

A. 4
B. 8
C. 16
D. 32

Sagot :

GinnyAnswer
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].
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