Solve Using the Quadratic Formula -4k^2-8k-3=-3-5k^2

$- 4 k^{2} - 8 k - 3 = - 3 - 5 k^{2}$

Step 1

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Add $3$ to both sides of the equation.

$- 4 k^{2} - 8 k - 3 + 3 = - 5 k^{2}$

Add $5 k^{2}$ to both sides of the equation.

$- 4 k^{2} - 8 k - 3 + 3 + 5 k^{2} = 0$

Simplify $- 4 k^{2} - 8 k - 3 + 3 + 5 k^{2}$ .

Combine the opposite terms in $- 4 k^{2} - 8 k - 3 + 3 + 5 k^{2}$ .

Add $- 3$ and $3$ .

$- 4 k^{2} - 8 k + 0 + 5 k^{2} = 0$

Add $- 4 k^{2} - 8 k$ and $0$ .

$- 4 k^{2} - 8 k + 5 k^{2} = 0$

Add $- 4 k^{2}$ and $5 k^{2}$ .

$k^{2} - 8 k = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = - 8$ , and $c = 0$ into the quadratic formula and solve for $k$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot 0)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$k = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot 0}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 0$ .

Multiply $- 4$ by $1$ .

$k = \frac{8 \pm \sqrt{64 - 4 \cdot 0}}{2 \cdot 1}$

Multiply $- 4$ by $0$ .

$k = \frac{8 \pm \sqrt{64 + 0}}{2 \cdot 1}$

Add $64$ and $0$ .

$k = \frac{8 \pm \sqrt{64}}{2 \cdot 1}$

Rewrite $64$ as $8^{2}$ .

$k = \frac{8 \pm \sqrt{8^{2}}}{2 \cdot 1}$

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

$k = \frac{8 \pm 8}{2 \cdot 1}$

Multiply $2$ by $1$ .

$k = \frac{8 \pm 8}{2}$

Simplify $\frac{8 \pm 8}{2}$ .

$k = 4 \pm 4$

Step 5

The final answer is the combination of both solutions.

$k = 8, 0$