Solve for w 5w^2=-17w-6

$5 w^{2} = - 17 w - 6$

Step 1

Add $17 w$ to both sides of the equation.

$5 w^{2} + 17 w = - 6$

Step 2

Add $6$ to both sides of the equation.

$5 w^{2} + 17 w + 6 = 0$

Step 3

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 5 \cdot 6 = 30$ and whose sum is $b = 17$ .

Factor $17$ out of $17 w$ .

$5 w^{2} + 17 (w) + 6 = 0$

Rewrite $17$ as $2$ plus $15$

$5 w^{2} + (2 + 15) w + 6 = 0$

Apply the distributive property.

$5 w^{2} + 2 w + 15 w + 6 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 w^{2} + 2 w) + 15 w + 6 = 0$

Factor out the greatest common factor (GCF) from each group.

$w (5 w + 2) + 3 (5 w + 2) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 w + 2$ .

$(5 w + 2) (w + 3) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$5 w + 2 = 0$

$w + 3 = 0$

Step 5

Set $5 w + 2$ equal to $0$ and solve for $w$ .

Set $5 w + 2$ equal to $0$ .

$5 w + 2 = 0$

Solve $5 w + 2 = 0$ for $w$ .

Subtract $2$ from both sides of the equation.

$5 w = - 2$

Divide each term in $5 w = - 2$ by $5$ and simplify.

Divide each term in $5 w = - 2$ by $5$ .

$\frac{5 w}{5} = \frac{- 2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 w}{5} = \frac{- 2}{5}$

Divide $w$ by $1$ .

$w = \frac{- 2}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$w = - \frac{2}{5}$

Step 6

Set $w + 3$ equal to $0$ and solve for $w$ .

Set $w + 3$ equal to $0$ .

$w + 3 = 0$

Subtract $3$ from both sides of the equation.

$w = - 3$

Step 7

The final solution is all the values that make $(5 w + 2) (w + 3) = 0$ true.

$w = - \frac{2}{5}, - 3$

Step 8

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{2}{5}, - 3$

Decimal Form:

$w = - 0.4, - 3$

Solve for w 5w^2=-17w-6

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