Question

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

x2 – 6x = 5

What value of c makes x2 − 24x + c a perfect square trinomial?

−144
−48
48
144

Answer 1

To complete the square in the given equation, add (6/2)² = 9 to both sides. The value of c that makes the second equation a perfect square trinomial is 9.

Step-by-step explanation:

To complete the square in the equation x² - 6x = 5, we need to add a constant term to both sides of the equation. The constant we add is half the coefficient of the x-term squared. In this case, the coefficient of the x-term is -6, so we add (6/2)² = 9 to both sides:

x² - 6x + 9 = 5 + 9

Now, we have a perfect square trinomial on the left side: (x - 3)² = 14. Therefore, the value of c that makes x² - 24x + c a perfect square trinomial is 9.