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 of numbers: −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, which states that if the product of two factors is zero, at least one of the factors must be 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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