Solve for s 5(s+8)^2-19(s+8)=4

Problem

5*(s+8)2−19*(s+8)=4

Solution

1. Substitute a new variable u=s+8 to simplify the quadratic equation.

5*u2−19*u=4

2. Rearrange the equation into standard quadratic form a*u2+b*u+c=0 by subtracting 4 from both sides.

5*u2−19*u−4=0

3. Factor the quadratic expression by finding two numbers that multiply to −20 (from 5×−4 and add to −19

(5*u+1)*(u−4)=0

4. Solve for u by setting each factor equal to zero.

5*u+1=0⇒u=−1/5

u−4=0⇒u=4

5. Back-substitute s+8 for u to find the values of s()

s+8=−1/5⇒s=−8−1/5=−41/5

s+8=4⇒s=4−8=−4

Final Answer

s=−41/5,−4

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