Find the Roots (Zeros) x^2+6x+9=0

Problem

x2+6*x+9=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 where a=1 b=6 and c=9

2. Factor the quadratic expression by looking for two numbers that multiply to c (9) and add to b (6).

3. Recognize that the expression is a perfect square trinomial since 3×3=9 and 3 + 3 = 6$.

4. Rewrite the equation in its factored form.

(x+3)*(x+3)=0

5. Apply the zero product property by setting the factor equal to zero.

x+3=0

6. Solve for x by subtracting 3 from both sides.

x=−3

Final Answer

x=−3

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