Solve x-x^2-2x+4

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

Factor

$$-\left(x-\frac{-\sqrt{17}-1}{2}\right)\left(x-\frac{\sqrt{17}-1}{2}\right)$$

Steps Using the Quadratic Formula

Combine x and -2x to get -x.

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

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.

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

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.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-\left(-1\right)±\sqrt{1+4\times 4}}{2\left(-1\right)}$$

Multiply 4 times 4.

$$x=\frac{-\left(-1\right)±\sqrt{1+16}}{2\left(-1\right)}$$

Add 1 to 16.

$$x=\frac{-\left(-1\right)±\sqrt{17}}{2\left(-1\right)}$$

The opposite of -1 is 1.

$$x=\frac{1±\sqrt{17}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{1±\sqrt{17}}{-2}$$

Now solve the equation x=\frac{1±\sqrt{17}}{-2} when ± is plus. Add 1 to \sqrt{17}.

$$x=\frac{\sqrt{17}+1}{-2}$$

Divide 1+\sqrt{17} by -2.

$$x=\frac{-\sqrt{17}-1}{2}$$

Now solve the equation x=\frac{1±\sqrt{17}}{-2} when ± is minus. Subtract \sqrt{17} from 1.

$$x=\frac{1-\sqrt{17}}{-2}$$

Divide 1-\sqrt{17} by -2.

$$x=\frac{\sqrt{17}-1}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1-\sqrt{17}}{2} for x_{1} and \frac{-1+\sqrt{17}}{2} for x_{2}.

$$-x^{2}-x+4=-\left(x-\frac{-\sqrt{17}-1}{2}\right)\left(x-\frac{\sqrt{17}-1}{2}\right)$$

Evaluate

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

Solution Steps

Combine x and -2x to get -x.

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