Solve by Factoring 2x^2-5x-3=0

Problem

2*x2−5*x−3=0

Solution

1. Identify the coefficients of the quadratic equation a*x2+b*x+c=0 where a=2 b=−5 and c=−3

2. Find two numbers that multiply to a⋅c=2⋅(−3)=−6 and add to b=−5 These numbers are −6 and 1

3. Rewrite the middle term −5*x using the two numbers found: 2*x2−6*x+x−3=0

4. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 2*x*(x−3)+1*(x−3)=0

5. Factor out the common binomial (x−3) to get the factored form: (2*x+1)*(x−3)=0

6. Apply the Zero Product Property by setting each factor equal to zero: 2*x+1=0 or x−3=0

7. Solve each linear equation for x x=−1/2 and x=3

Final Answer

x=−1/2,3

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