Solve by Factoring x^2-2x-15=0

Problem

x2−2*x−15=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=−15

2. Find two numbers that multiply to c (−15 and add to b (−2. These numbers are −5 and 3

3. Rewrite the quadratic expression as a product of two binomials using the numbers found in the previous step.

(x−5)*(x+3)=0

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

x−5=0

x+3=0

5. Solve each linear equation for x

x=5

x=−3

Final Answer

x=5,−3

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