Rewrite by completing the square
x2 + x + 1
x^2+x+1
x^2+2(1/2)x + (1/2)^2 + 3/4
(x + 1/2)^2 + 3/4
To rewrite the quadratic expression x^2 + x + 1 by completing the square, follow these steps:
1. Take the coefficient of x, which is 1, and divide it by 2: (1 ÷ 2 = 1/2).
2. Square the result from step 1: (1/2)^2 = 1/4.
3. Add the result from step 2 to both sides of the equation: x^2 + x + 1 + 1/4 = 1 + 1/4.
4. Simplify the right side of the equation: x^2 + x + 5/4 = 4/4 + 1/4.
5. On the left side of the equation, the first three terms can be factored: (x + 1/2)^2 = 5/4.
Therefore, the completed square form of the quadratic expression x^2 + x + 1 is (x + 1/2)^2 = 5/4.