Question

Can someone please help me

Answer 1

Answer:

1. The marked answer is correct.

2. The only equivalent equation is the 2nd one: x^2 -12x +36 = 28

Step-by-step explanation:

The square of a binomial is ...

(x -a)^2 = x^2 -2ax +a^2

This tells you the constant term in the perfect square trinomial is the square of half the x-coefficient.

1. The x-coefficient is -8, so half that is -4. The square of -4 is 16. To complete the square, the added constant term must be 16, the marked answer.

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2. The x-coefficient is -12, so the square of half that is (-6)^2 = 36. Adding 36 to the equation gives ...

x^2 -12x +36 = 28 . . . . . . matches the 2nd choice

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The rule that makes algebra work is this: whatever you do on one side of the equal sign must also be done on the other side.

If you add 36 on one side of the equation, you must add 36 on the other side. Of course addition of signed numbers is done in the usual way: 36 + (-8) = 28.