Algebra Examples

$2 x^{2} + 7 x - 2 = - x^{2} + 2 x$

Step 1

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

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

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

$2 x^{2} + 7 x - 2 + x^{2} = 2 x$

Step 1.1.2

Subtract $2 x$ from both sides of the equation.

$2 x^{2} + 7 x - 2 + x^{2} - 2 x = 0$

Step 1.2

Simplify $2 x^{2} + 7 x - 2 + x^{2} - 2 x$ .

Tap for more steps...

Step 1.2.1

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

$3 x^{2} + 7 x - 2 - 2 x = 0$

Step 1.2.2

Subtract $2 x$ from $7 x$ .

$3 x^{2} + 5 x - 2 = 0$

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 $a = 3$ , $b = 5$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (3 \cdot - 2)}}{2 \cdot 3}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Raise $5$ to the power of $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 3 \cdot - 2}}{2 \cdot 3}$

Step 4.1.2

Multiply $- 4 \cdot 3 \cdot - 2$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{- 5 \pm \sqrt{25 - 12 \cdot - 2}}{2 \cdot 3}$

Step 4.1.2.2

Multiply $- 12$ by $- 2$ .

$x = \frac{- 5 \pm \sqrt{25 + 24}}{2 \cdot 3}$

Step 4.1.3

Add $25$ and $24$ .

$x = \frac{- 5 \pm \sqrt{49}}{2 \cdot 3}$

Step 4.1.4

Rewrite $49$ as $7^{2}$ .

$x = \frac{- 5 \pm \sqrt{7^{2}}}{2 \cdot 3}$

Step 4.1.5

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

$x = \frac{- 5 \pm 7}{2 \cdot 3}$

Step 4.2

Multiply $2$ by $3$ .

$x = \frac{- 5 \pm 7}{6}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{1}{3}, - 2$