Algebra Examples

$6 x^{2} - 2 + x = x$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $x$ from both sides of the equation.

$6 x^{2} - 2 + x - x = 0$

Step 1.2

Combine the opposite terms in $6 x^{2} - 2 + x - x$ .

Tap for more steps...

Step 1.2.1

Subtract $x$ from $x$ .

$6 x^{2} - 2 + 0 = 0$

Step 1.2.2

Add $6 x^{2} - 2$ and $0$ .

$6 x^{2} - 2 = 0$

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 $a = 6$ , $b = 0$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (6 \cdot - 2)}}{2 \cdot 6}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 6 \cdot - 2}}{2 \cdot 6}$

Step 4.1.2

Multiply $- 4 \cdot 6 \cdot - 2$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $6$ .

$x = \frac{0 \pm \sqrt{0 - 24 \cdot - 2}}{2 \cdot 6}$

Step 4.1.2.2

Multiply $- 24$ by $- 2$ .

$x = \frac{0 \pm \sqrt{0 + 48}}{2 \cdot 6}$

Step 4.1.3

Add $0$ and $48$ .

$x = \frac{0 \pm \sqrt{48}}{2 \cdot 6}$

Step 4.1.4

Rewrite $48$ as $4^{2} \cdot 3$ .

Tap for more steps...

Step 4.1.4.1

Factor $16$ out of $48$ .

$x = \frac{0 \pm \sqrt{16 (3)}}{2 \cdot 6}$

Step 4.1.4.2

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm \sqrt{4^{2} \cdot 3}}{2 \cdot 6}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{0 \pm 4 \sqrt{3}}{2 \cdot 6}$

Step 4.2

Multiply $2$ by $6$ .

$x = \frac{0 \pm 4 \sqrt{3}}{12}$

Step 4.3

Simplify $\frac{0 \pm 4 \sqrt{3}}{12}$ .

$x = \frac{\pm \sqrt{3}}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\pm \sqrt{3}}{3}$

Decimal Form:

$x = 0.57735026 \dots, - 0.57735026 \dots$