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Let x^2 + 11x = 3

What values make an equivalent number sentence after completing the square?


x^2 + 11x + _____ = _____

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x^2+11x+x+36=39+x


x^2+12x+36=39+x


(x+6)^2=39+x

The value that makes an equivalent number sentence after completing the square is (x+6)²=39+x.

What is an equivalent number sentence?

An equivalent number sentence is an equation where both the sides of the equation, therefore, the expressions are true.

It is given that the value of x²+11x=3, and we need an equivalent number sentence after completing the square, therefore, the equation can be written as,

\(x^2 +11x = 3\)

We can write 3 as 39-36 and also, 11x can be written 12x-x, so the equation can be modeled as,

\(x^2 +12x - x = 39-36\\\)

Now, take 36 on the left side to make the equation a perfect square while, while x on the right side,

\(x^2 +12x +36=39+x\\\\(x+6)^2 = 39+x\)

Hence, the value that makes an equivalent number sentence after completing the square is (x+6)²=39+x.

learn more about Equivalent Number Sentence:

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