Solve by Factoring x^2-3x-10=0

Problem

x2−3*x−10=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 where a=1 b=−3 and c=−10

2. Find two numbers that multiply to c (−10 and add to b (−3.

3. Determine that the two numbers are −5 and 2 since (−5)*(2)=−10 and −5+2=−3

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

(x−5)*(x+2)=0

5. Apply the zero product property by setting each factor equal to zero.

x−5=0

x+2=0

6. Solve each linear equation for x

x=5

x=−2

Final Answer

x2−3*x−10=0⇒x=5,−2

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