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Solve for $s$ . $\newline$ $4s^2 - 35s - 9 = 0$ $\newline$ Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $\newline$ $s =$ ____

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Solve polynomial equations

Full solution

Q. Solve for

s

.

\newline

4s^2 - 35s - 9 = 0

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

s =

____

Rewrite equation with split terms: Now, rewrite the equation by splitting the middle term using the numbers we found: $4s^2 - 36s + s - 9 = 0$ .
Factor by grouping: Next, factor by grouping: $(4s^2 - 36s) + (s - 9)$ . Take out the common factor from each group: $4s(s - 9) + 1(s - 9)$ .
Common factor extraction: Now we have a common factor of $(s - 9)$ , so factor it out: $(4s + 1)(s - 9) = 0$ .
Factor out common factor: Set each factor equal to zero: $4s + 1 = 0$ and $s - 9 = 0$ .
Set factors equal to zero: Solve $4s + 1 = 0$ : Subtract $1$ from both sides to get $4s = -1$ , then divide by $4$ to get $s = -\frac{1}{4}$ .
Solve for $4s + 1$ : Solve $s - 9 = 0$ : Add $9$ to both sides to get $s = 9$ .

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