Solve by Factoring 8x^2+10x-7=0

Problem

8*x2+10*x−7=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 where a=8 b=10 and c=−7

2. Find two numbers that multiply to a⋅c=8⋅(−7)=−56 and add to b=10

3. Determine the pair of numbers, which are 14 and −4 since 14⋅(−4)=−56 and 14 + (-4) = 10$.

4. Rewrite the middle term 10*x using the two numbers found: 8*x2+14*x−4*x−7=0

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 2*x*(4*x+7)−1*(4*x+7)=0

6. Factor out the common binomial (4*x+7) to get (2*x−1)*(4*x+7)=0

7. Apply the zero product property by setting each factor equal to zero: 2*x−1=0 or 4*x+7=0

8. Solve each linear equation for x

2*x=1⇒x=1/2

4*x=−7⇒x=−7/4

Final Answer

x=1/2,−7/4

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