Solve for x 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. Factor the quadratic expression by finding two numbers that multiply to 6 and add to −5 These numbers are −2 and −3

3. Rewrite the equation in factored form:

(x−2)*(x−3)=0

4. Apply the zero product property by setting each factor equal to zero:

x−2=0

x−3=0

5. Solve for x in each linear equation:

x=2

x=3

Final Answer

x=2,3

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