Solve by Factoring z^2+2z-35=0

Problem

z2+2*z−35=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*z2+b*z+c=0 where a=1 b=2 and c=−35

2. Find two numbers that multiply to c (−35 and add to b (2.

3. Determine that the two numbers are 7 and −5 because 7⋅(−5)=−35 and 7 + (-5) = 2$.

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

(z+7)*(z−5)=0

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

z+7=0

z−5=0

6. Solve each linear equation for z

z=−7

z=5

Final Answer

z2+2*z−35=0⇒z=−7,5

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