Find the Roots (Zeros) 2x^2-4=16x

$2 x^{2} - 4 = 16 x$

Step 1

Subtract $16 x$ from both sides of the equation.

$2 x^{2} - 4 - 16 x = 0$

Step 2

Factor the left side of the equation.

Factor $2$ out of $2 x^{2} - 4 - 16 x$ .

Factor $2$ out of $2 x^{2}$ .

$2 (x^{2}) - 4 - 16 x = 0$

Factor $2$ out of $- 4$ .

$2 x^{2} + 2 \cdot - 2 - 16 x = 0$

Factor $2$ out of $- 16 x$ .

$2 x^{2} + 2 \cdot - 2 + 2 (- 8 x) = 0$

Factor $2$ out of $2 x^{2} + 2 \cdot - 2$ .

$2 (x^{2} - 2) + 2 (- 8 x) = 0$

Factor $2$ out of $2 (x^{2} - 2) + 2 (- 8 x)$ .

$2 (x^{2} - 2 - 8 x) = 0$

Reorder terms.

$2 (x^{2} - 8 x - 2) = 0$

Step 3

Divide each term in $2 (x^{2} - 8 x - 2) = 0$ by $2$ and simplify.

Divide each term in $2 (x^{2} - 8 x - 2) = 0$ by $2$ .

$\frac{2 (x^{2} - 8 x - 2)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (x^{2} - 8 x - 2)}{2} = \frac{0}{2}$

Divide $x^{2} - 8 x - 2$ by $1$ .

$x^{2} - 8 x - 2 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

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

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = 1$ , $b = - 8$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

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

Step 6

Simplify.

Simplify the numerator.

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

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

Multiply $- 4 \cdot 1 \cdot - 2$ .

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $- 2$ .

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

Add $64$ and $8$ .

$x = \frac{8 \pm \sqrt{72}}{2 \cdot 1}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$x = \frac{8 \pm \sqrt{36 (2)}}{2 \cdot 1}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{8 \pm \sqrt{6^{2} \cdot 2}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{8 \pm 6 \sqrt{2}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8 \pm 6 \sqrt{2}}{2}$

Simplify $\frac{8 \pm 6 \sqrt{2}}{2}$ .

$x = 4 \pm 3 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 4 \pm 3 \sqrt{2}$

Decimal Form:

$x = 8.24264068 \dots, - 0.24264068 \dots$

Step 8

Find the Roots (Zeros) 2x^2-4=16x

Related Questions

Support LCMGCF.com by disabling your adblocker.