Solve 4x^2+4x-4+x^2

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

Factor

$$5\left(x-\frac{-2\sqrt{6}-2}{5}\right)\left(x-\frac{2\sqrt{6}-2}{5}\right)$$

Steps Using the Quadratic Formula

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$factor(5x^{2}+4x-4)$$

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.

$$5x^{2}+4x-4=0$$

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.

$$x=\frac{-4±\sqrt{4^{2}-4\times 5\left(-4\right)}}{2\times 5}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\times 5\left(-4\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-4±\sqrt{16-20\left(-4\right)}}{2\times 5}$$

Multiply -20 times -4.

$$x=\frac{-4±\sqrt{16+80}}{2\times 5}$$

Add 16 to 80.

$$x=\frac{-4±\sqrt{96}}{2\times 5}$$

Take the square root of 96.

$$x=\frac{-4±4\sqrt{6}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{-4±4\sqrt{6}}{10}$$

Now solve the equation x=\frac{-4±4\sqrt{6}}{10} when ± is plus. Add -4 to 4\sqrt{6}.

$$x=\frac{4\sqrt{6}-4}{10}$$

Divide -4+4\sqrt{6} by 10.

$$x=\frac{2\sqrt{6}-2}{5}$$

Now solve the equation x=\frac{-4±4\sqrt{6}}{10} when ± is minus. Subtract 4\sqrt{6} from -4.

$$x=\frac{-4\sqrt{6}-4}{10}$$

Divide -4-4\sqrt{6} by 10.

$$x=\frac{-2\sqrt{6}-2}{5}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-2+2\sqrt{6}}{5} for x_{1} and \frac{-2-2\sqrt{6}}{5} for x_{2}.

$$5x^{2}+4x-4=5\left(x-\frac{2\sqrt{6}-2}{5}\right)\left(x-\frac{-2\sqrt{6}-2}{5}\right)$$

Evaluate

$$5x^{2}+4x-4$$

Solution Steps

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$5x^{2}+4x-4$$