Identify the number that needs to be added to both sides of the equation x2 + 4x = 96 to complete the square.?

Add 4.

Dear, I can tell you the exact way to make ANY quadratic a perfect square.

Here goes the steps for a quadratic equation ax^2+bx+c=0

1. Make the coefficient of x^2 equal to 1. This is done by taking the coefficent 'a' common from the whole quadratic.

2. Now add and subtract the square of half the coefficient of x i.e (b/2)^2

3. You can then guess it out yourself then the perfect square.

For your question:

Consider x^2 + 4x

The coefficient of x^2 is already equal to 1 so no worries.

Now add and subtract by (4/2)^2 which is equal to 4.

Hey, the second step is also called as "add the square of half the coefficient of x both sides of the equation" because when you subtract the required number it will become positive when it goes to the other side.

For more tips n tricks you can always contact me.

X^2+4x+4=96+4

(x+2)^2=10^2

4

4

x² + 4x = 96

Take the coefficient of the x term

(+4)

divide by two

(+4/2)

and square the result

(+4/2)²

This reduces to 4, so the answer is #3. But I never reduce it completely, (a) because it would have to be undone in the next steps, (b) you might forget which sign to use.

For example:

x² - 4x = 0

To complete the square, you add (-4/2)² to both sides. That can be reduced to 4, but then you lose the minus sign that you need later. Better to use (-2)²:

x² - 4x + (-2)² = 0 + (-2)²

(x-2)² = 4

When you are completing the square, the number you add to the function is (b/2)^2

In this case b=4

(4/2)^2=4

Therefore your answer if choice 3

(x² + 4x + 4) = 100

(x + 2)² = 100

x + 2 = ± 10

x = 8 , x = - 12

OPTION 3

the answer is 4.

then the lefh hand side will be x^2+4x+4 = (x+2)^2

and the right hand side will be 100 = 10^2.

x2+4x=96

since

a2+b2+2ab=(a+b)2

so

(x)2+2(x)(2)+(2)2=96+(2)2

(x+2)2=96+4

(x+2)2=100

taking square root

x+2=10

x=10-2

x=8

hey its the rite answer why ur choices didnt include this answer

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