Complete the Square x^2+10x+13

Problem

x^2+10*x+13

Solution

1. Identify the coefficient of the linear term x which is 10

2. Calculate the value needed to create a perfect square trinomial by taking half of that coefficient and squaring it: (10/2)^2=5^2=25

3. Add and subtract this value within the expression to maintain equality: x^2+10*x+25−25+13

4. Group the first three terms as a perfect square and combine the remaining constants: (x+5)^2−12

Final Answer

x^2+10*x+13=(x+5)^2−12

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