Find the Perfect Square Trinomial x^2+9x

Problem

$x^2+9x$

Solution

1. Identify the coefficient of the linear term $x$ which is $b=9$

2. Divide the coefficient $b$ by $2$ to get $\frac{9}{2}$

3. Square the result of the division to find the constant term needed to complete the square: ${\left(\frac{9}{2}\right)}^2=\frac{81}{4}$

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: ${(x+\frac{9}{2})}^2$

Final Answer

$x^2+9x+\frac{81}{4}={(x+\frac{9}{2})}^2$

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