Find the Perfect Square Trinomial x^2+2x

Problem

x^2+2*x

Solution

1. Identify the coefficients of the quadratic expression in the form x^2+b*x where b=2

2. Calculate the value needed to complete the square by taking half of the linear coefficient b and squaring it: (b/2)^2

3. Substitute the value of b into the formula: (2/2)^2=1^2=1

4. Add this constant to the original expression to form a perfect square trinomial.

5. Factor the resulting trinomial into the square of a binomial: (x+b/2)^2

Final Answer

x^2+2*x+1=(x+1)^2

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