Complete the square for the binomial. Then factor the resulting perfect square trinomial?

Question

X2+1/3x

Answer 1

x² + (1/3)x

To complete the square, you take the coefficient on x, which is 1/3, divide it in half (1/6) and square it (1/36).

Add this and subtract it:

(x² + (1/3)x + 1/36) - 1/36

The part in the parentheses is in the following form:
a² + 2ab + b²

[ (x² + 2(1/6)x + (1/6)² ] - 1/36

So it is ready to be written as (a + b)²

= (x + 1/6)² - 1/36

Answer 2

x^2 + (a million / 3)x + _______ - _______ Take the coefficient of the x term: (a million / 3) Divide it by 2. (a million / 3) / 2 = (a million / 6) sq. it: (a million / 6)^2 = (a million^2 / 6^2) = (a million / 36) Fill the two blanks with this fee: x^2 + (a million / 3)x + (a million / 36) - (a million / 36) ingredient. [x + (a million / 6)]^2 - (a million / 36) answer: [x + (a million / 6)]^2 - (a million / 36) ------------------ examine: [x + (a million / 6)]^2 - (a million / 36) = [x + (a million / 6)][x + (a million / 6)] - (a million / 36) = x(x) + x(a million / 6) + (a million / 6)x + (a million / 6)(a million / 6) - (a million / 36) = x^2 + (x / 6) + (x / 6) + (a million / 36) - (a million / 36) = x^2 + (2x / 6) = x^2 + (1x / 3) = x^2 + (a million / 3)x = actual