Solve for x -12=11x^2+28x

$- 12 = 11 x^{2} + 28 x$

Step 1

Rewrite the equation as $11 x^{2} + 28 x = - 12$ .

$11 x^{2} + 28 x = - 12$

Step 2

Add $12$ to both sides of the equation.

$11 x^{2} + 28 x + 12 = 0$

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 $a \cdot c = 11 \cdot 12 = 132$ and whose sum is $b = 28$ .

Factor $28$ out of $28 x$ .

$11 x^{2} + 28 (x) + 12 = 0$

Rewrite $28$ as $6$ plus $22$

$11 x^{2} + (6 + 22) x + 12 = 0$

Apply the distributive property.

$11 x^{2} + 6 x + 22 x + 12 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(11 x^{2} + 6 x) + 22 x + 12 = 0$

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

$x (11 x + 6) + 2 (11 x + 6) = 0$

Factor the polynomial by factoring out the greatest common factor, $11 x + 6$ .

$(11 x + 6) (x + 2) = 0$

Step 4

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

$11 x + 6 = 0$

$x + 2 = 0$

Step 5

Set $11 x + 6$ equal to $0$ and solve for $x$ .

Set $11 x + 6$ equal to $0$ .

$11 x + 6 = 0$

Solve $11 x + 6 = 0$ for $x$ .

Subtract $6$ from both sides of the equation.

$11 x = - 6$

Divide each term in $11 x = - 6$ by $11$ and simplify.

Divide each term in $11 x = - 6$ by $11$ .

$\frac{11 x}{11} = \frac{- 6}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{- 6}{11}$

Divide $x$ by $1$ .

$x = \frac{- 6}{11}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{6}{11}$

Step 6

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 7

The final solution is all the values that make $(11 x + 6) (x + 2) = 0$ true.

$x = - \frac{6}{11}, - 2$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{6}{11}, - 2$

Decimal Form:

$x = - 0.\overline{54}, - 2$

Solve for x -12=11x^2+28x

Related Questions

Support LCMGCF.com by disabling your adblocker.