Solve x^2-4x^2+4+8x

$$x ^ { 2 } - 4 x ^ { 2 } + 4 + 8 x$$

Factor

$$-3\left(x-\frac{4-2\sqrt{7}}{3}\right)\left(x-\frac{2\sqrt{7}+4}{3}\right)$$

Steps Using the Quadratic Formula

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$factor(-3x^{2}+4+8x)$$

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.

$$-3x^{2}+8x+4=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-3\right)\times 4}}{2\left(-3\right)}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-3\right)\times 4}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{-8±\sqrt{64+12\times 4}}{2\left(-3\right)}$$

Multiply 12 times 4.

$$x=\frac{-8±\sqrt{64+48}}{2\left(-3\right)}$$

Add 64 to 48.

$$x=\frac{-8±\sqrt{112}}{2\left(-3\right)}$$

Take the square root of 112.

$$x=\frac{-8±4\sqrt{7}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{-8±4\sqrt{7}}{-6}$$

Now solve the equation x=\frac{-8±4\sqrt{7}}{-6} when ± is plus. Add -8 to 4\sqrt{7}.

$$x=\frac{4\sqrt{7}-8}{-6}$$

Divide -8+4\sqrt{7} by -6.

$$x=\frac{4-2\sqrt{7}}{3}$$

Now solve the equation x=\frac{-8±4\sqrt{7}}{-6} when ± is minus. Subtract 4\sqrt{7} from -8.

$$x=\frac{-4\sqrt{7}-8}{-6}$$

Divide -8-4\sqrt{7} by -6.

$$x=\frac{2\sqrt{7}+4}{3}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{4-2\sqrt{7}}{3} for x_{1} and \frac{4+2\sqrt{7}}{3} for x_{2}.

$$-3x^{2}+8x+4=-3\left(x-\frac{4-2\sqrt{7}}{3}\right)\left(x-\frac{2\sqrt{7}+4}{3}\right)$$

Evaluate

$$4+8x-3x^{2}$$

Solution Steps

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+4+8x$$