Solve by Factoring x^2-5x+6=0

Problem

x2−5*x+6=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 where a=1 b=−5 and c=6

2. Find two numbers that multiply to the constant term c=6 and add to the linear coefficient b=−5

3. Determine the factors by testing pairs of numbers: (−2)×(−3)=6 and (−2)+(−3)=−5

4. Rewrite the quadratic expression as a product of two binomials using these numbers.

(x−2)*(x−3)=0

5. Apply the Zero Product Property, which states that if the product of two factors is zero, at least one of the factors must be zero.

x−2=0

x−3=0

6. Solve each linear equation for x

x=2

x=3

Final Answer

x2−5*x+6=0⇒x=2,3

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