Solve x^2-frac{sqrt{2}}{2}x+1

$${ x }^{ 2 } - \frac{ \sqrt{ 2 } }{ 2 } x+1$$

Evaluate

$$x^{2}-\frac{\sqrt{2}x}{2}+1$$

Short Solution Steps

Express \frac{\sqrt{2}}{2}x as a single fraction.

$$x^{2}-\frac{\sqrt{2}x}{2}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{2}{2}.

$$\frac{2x^{2}}{2}-\frac{\sqrt{2}x}{2}+1$$

Since \frac{2x^{2}}{2} and \frac{\sqrt{2}x}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x^{2}-\sqrt{2}x}{2}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\frac{2x^{2}-\sqrt{2}x}{2}+\frac{2}{2}$$

Since \frac{2x^{2}-\sqrt{2}x}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{2x^{2}-\sqrt{2}x+2}{2}$$

Factor

$$\frac{\sqrt{2}\left(\sqrt{2}x^{2}-x+\sqrt{2}\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{2x^{2}-\sqrt{2}x+2}{2}$$

Consider 2x^{2}-\sqrt{2}x+2. Factor out \sqrt{2}.

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

Rewrite the complete factored expression. Polynomial \sqrt{2}x^{2}-x+\sqrt{2} is not factored since it does not have any rational roots.

$$\frac{\sqrt{2}\left(\sqrt{2}x^{2}-x+\sqrt{2}\right)}{2}$$