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

Problem

x2−6*x+5=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=5

2. Find two numbers that multiply to c (5 and add to b (−6.

3. Determine that the two numbers are −1 and −5 because (−1)×(−5)=5 and (−1)+(−5)=−6

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

(x−1)*(x−5)=0

5. Apply the Zero Product Property by setting each factor equal to zero.

x−1=0

x−5=0

6. Solve each linear equation for x

x=1

x=5

Final Answer

x=1,5

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