Solve for k k^2-31-2k=-6-3k^2-2k

$k^{2} - 31 - 2 k = - 6 - 3 k^{2} - 2 k$

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

Add $3 k^{2}$ to both sides of the equation.

$k^{2} - 31 - 2 k + 3 k^{2} = - 6 - 2 k$

Add $2 k$ to both sides of the equation.

$k^{2} - 31 - 2 k + 3 k^{2} + 2 k = - 6$

Combine the opposite terms in $k^{2} - 31 - 2 k + 3 k^{2} + 2 k$ .

Add $- 2 k$ and $2 k$ .

$k^{2} - 31 + 3 k^{2} + 0 = - 6$

Add $k^{2} - 31 + 3 k^{2}$ and $0$ .

$k^{2} - 31 + 3 k^{2} = - 6$

Add $k^{2}$ and $3 k^{2}$ .

$4 k^{2} - 31 = - 6$

Move all terms not containing $k$ to the right side of the equation.

Add $31$ to both sides of the equation.

$4 k^{2} = - 6 + 31$

Add $- 6$ and $31$ .

$4 k^{2} = 25$

Divide each term in $4 k^{2} = 25$ by $4$ and simplify.

Divide each term in $4 k^{2} = 25$ by $4$ .

$\frac{4 k^{2}}{4} = \frac{25}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 k^{2}}{4} = \frac{25}{4}$

Divide $k^{2}$ by $1$ .

$k^{2} = \frac{25}{4}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$k = \pm \sqrt{\frac{25}{4}}$

Simplify $\pm \sqrt{\frac{25}{4}}$ .

Rewrite $\sqrt{\frac{25}{4}}$ as $\frac{\sqrt{25}}{\sqrt{4}}$ .

$k = \pm \frac{\sqrt{25}}{\sqrt{4}}$

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$k = \pm \frac{\sqrt{5^{2}}}{\sqrt{4}}$

Pull terms out from under the radical, assuming positive real numbers.

$k = \pm \frac{5}{\sqrt{4}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$k = \pm \frac{5}{\sqrt{2^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$k = \pm \frac{5}{2}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

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

Next, use the negative value of the $\pm$ to find the second solution.

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

The complete solution is the result of both the positive and negative portions of the solution.

$k = \frac{5}{2}, - \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$k = \frac{5}{2}, - \frac{5}{2}$

Decimal Form:

$k = 2.5, - 2.5$

Mixed Number Form:

$k = 2 \frac{1}{2}, - 2 \frac{1}{2}$

Solve for k k^2-31-2k=-6-3k^2-2k

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