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Mia is solving the equation x2 – 12x = 1. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?


9


-9


36


8

Sagot :

Adioabiolaidn

The value to be added to both sides of the equation to make the left side a perfect square trinomial is; -36.

To make the equation x2 – 12x = 1 look similar to the completing the square kind of expression where the left hand side of the equation becomes a perfect square, we must do the following;

  • First, the completing the square method usually takes the form;

  • x² + bx = (x + b/2)² + c

In this scenario, the term (x² - 12x) can be rewritten as; (x - 6)² - 36.

This so because the expansion of (x - 6)² becomes;

  • x² - 12x + 36.

Therefore, there's a need to subtract 36 from both sides of the equation so that the equation x2 – 12x = 1 is retained.

Therefore, the value to be added to both sides of the equation to make the left side a perfect square trinomial is; -36.

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