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

Problem

x2+2*x−8=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 where a=1 b=2 and c=−8

2. Find two numbers that multiply to c (which is −8 and add to b (which is 2.

3. Determine the factors by testing pairs: 4 and −2 satisfy both conditions because 4⋅(−2)=−8 and 4 + (-2) = 2$.

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

(x+4)*(x−2)=0

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

x+4=0

x−2=0

6. Solve each linear equation for x

x=−4

x=2

Final Answer

x=−4,2

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