Solve for w 19w^2-30w+8=-6w^2

$19 w^{2} - 30 w + 8 = - 6 w^{2}$

Step 1

Move all terms containing $w$ to the left side of the equation.

Add $6 w^{2}$ to both sides of the equation.

$19 w^{2} - 30 w + 8 + 6 w^{2} = 0$

Add $19 w^{2}$ and $6 w^{2}$ .

$25 w^{2} - 30 w + 8 = 0$

Step 2

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 $a \cdot c = 25 \cdot 8 = 200$ and whose sum is $b = - 30$ .

Factor $- 30$ out of $- 30 w$ .

$25 w^{2} - 30 w + 8 = 0$

Rewrite $- 30$ as $- 10$ plus $- 20$

$25 w^{2} + (- 10 - 20) w + 8 = 0$

Apply the distributive property.

$25 w^{2} - 10 w - 20 w + 8 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(25 w^{2} - 10 w) - 20 w + 8 = 0$

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

$5 w (5 w - 2) - 4 (5 w - 2) = 0$

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

$(5 w - 2) (5 w - 4) = 0$

Step 3

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

$5 w - 2 = 0$

$5 w - 4 = 0$

Step 4

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 $w$ .

Add $2$ to 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 $1$ .

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

Step 5

Set $5 w - 4$ equal to $0$ and solve for $w$ .

Set $5 w - 4$ equal to $0$ .

$5 w - 4 = 0$

Solve $5 w - 4 = 0$ for $w$ .

Add $4$ to both sides of the equation.

$5 w = 4$

Divide each term in $5 w = 4$ by $5$ and simplify.

Divide each term in $5 w = 4$ by $5$ .

$\frac{5 w}{5} = \frac{4}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 w}{5} = \frac{4}{5}$

Divide $w$ by $1$ .

$w = \frac{4}{5}$

Step 6

The final solution is all the values that make $(5 w - 2) (5 w - 4) = 0$ true.

$w = \frac{2}{5}, \frac{4}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$w = \frac{2}{5}, \frac{4}{5}$

Decimal Form:

$w = 0.4, 0.8$

Solve for w 19w^2-30w+8=-6w^2

Related Questions

Support LCMGCF.com by disabling your adblocker.