Solve by Factoring x^2-6x+9=0

Problem

x2−6*x+9=0

Solution

1. Identify the quadratic expression on the left side of the equation, which is in the form a*x2+b*x+c

2. Find two numbers that multiply to the constant term 9 and add to the linear coefficient −6

3. Determine that the numbers are −3 and −3 since (−3)×(−3)=9 and (−3)+(−3)=−6

4. Rewrite the quadratic as a squared binomial based on these factors.

(x−3)*(x−3)=0

(x−3)2=0

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

x−3=0

6. Solve for x by adding 3 to both sides.

x=3

Final Answer

x2−6*x+9=0⇒x=3

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