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

Problem

2*x2+5*x−3=0

Solution

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

2. Find two numbers that multiply to a⋅c=−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 (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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