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What is the missing constant term in the perfect square that starts with x^(2)+6x ?

What is the missing constant term in the perfect square that starts with x2+6xx^{2}+6x ?

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Full solution

Q. What is the missing constant term in the perfect square that starts with x2+6xx^{2}+6x ?
  1. Find Coefficient of x: To complete the square for the expression x2+6xx^2 + 6x, we need to find a number that, when added to x2+6xx^2 + 6x, turns it into a perfect square trinomial. The perfect square trinomial will have the form (x+a)2(x + a)^2, where aa is half of the coefficient of xx. In this case, the coefficient of xx is 66.
  2. Calculate Half of Coefficient: We calculate half of the coefficient of xx, which is 62=3\frac{6}{2} = 3.
  3. Square the Value: Now we square the value we found in the previous step to get the constant term that completes the square. Squaring 33 gives us 32=93^2 = 9.
  4. Complete the Square: The constant term that completes the square for the expression x2+6xx^2 + 6x is 99. Adding this term to the expression gives us the perfect square trinomial (x+3)2(x + 3)^2.

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