Solve 2div2x^2+4x-2=

$$2 \div 2 { x }^{ 2 } +4x-2=$$

Evaluate

$$x^{2}+4x-2$$

Solution Steps

Divide 2 by 2 to get 1.

$$1x^{2}+4x-2$$

For any term t, t\times 1=t and 1t=t.

$$x^{2}+4x-2$$

Factor

$$\left(x-\left(-\sqrt{6}-2\right)\right)\left(x-\left(\sqrt{6}-2\right)\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

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

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-2\right)}}{2}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\left(-2\right)}}{2}$$

Multiply -4 times -2.

$$x=\frac{-4±\sqrt{16+8}}{2}$$

Add 16 to 8.

$$x=\frac{-4±\sqrt{24}}{2}$$

Take the square root of 24.

$$x=\frac{-4±2\sqrt{6}}{2}$$

Now solve the equation x=\frac{-4±2\sqrt{6}}{2} when ± is plus. Add -4 to 2\sqrt{6}.

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

Divide -4+2\sqrt{6} by 2.

$$x=\sqrt{6}-2$$

Now solve the equation x=\frac{-4±2\sqrt{6}}{2} when ± is minus. Subtract 2\sqrt{6} from -4.

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

Divide -4-2\sqrt{6} by 2.

$$x=-\sqrt{6}-2$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -2+\sqrt{6} for x_{1} and -2-\sqrt{6} for x_{2}.

$$x^{2}+4x-2=\left(x-\left(\sqrt{6}-2\right)\right)\left(x-\left(-\sqrt{6}-2\right)\right)$$