Solve for x x^2+21x=11-x^2

$x^{2} + 21 x = 11 - x^{2}$

Step 1

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

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

$x^{2} + 21 x + x^{2} = 11$

Add $x^{2}$ and $x^{2}$ .

$2 x^{2} + 21 x = 11$

Step 2

Subtract $11$ from both sides of the equation.

$2 x^{2} + 21 x - 11 = 0$

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 $a \cdot c = 2 \cdot - 11 = - 22$ and whose sum is $b = 21$ .

Factor $21$ out of $21 x$ .

$2 x^{2} + 21 (x) - 11 = 0$

Rewrite $21$ as $- 1$ plus $22$

$2 x^{2} + (- 1 + 22) x - 11 = 0$

Apply the distributive property.

$2 x^{2} - 1 x + 22 x - 11 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 1 x) + 22 x - 11 = 0$

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

$x (2 x - 1) + 11 (2 x - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$(2 x - 1) (x + 11) = 0$

Step 4

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

$2 x - 1 = 0$

$x + 11 = 0$

Step 5

Set $2 x - 1$ equal to $0$ and solve for $x$ .

Set $2 x - 1$ equal to $0$ .

$2 x - 1 = 0$

Solve $2 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$2 x = 1$

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Step 6

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

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

$x + 11 = 0$

Subtract $11$ from both sides of the equation.

$x = - 11$

Step 7

The final solution is all the values that make $(2 x - 1) (x + 11) = 0$ true.

$x = \frac{1}{2}, - 11$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}, - 11$

Decimal Form:

$x = 0.5, - 11$

Solve for x x^2+21x=11-x^2

Related Questions

Support LCMGCF.com by disabling your adblocker.