Solve 1/4x^2-x+1leq0

$$\frac { 1 } { 4 } x ^ { 2 } - x + 1 \leq 0$$

Solve for x

$$x=2$$

Steps Using the Quadratic Formula

To solve the inequality, factor the left hand side. 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.

$$\frac{1}{4}x^{2}-x+1=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute \frac{1}{4} for a, -1 for b, and 1 for c in the quadratic formula.

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

Do the calculations.

$$x=\frac{1±0}{\frac{1}{2}}$$

Solutions are the same.

$$x=2$$

Rewrite the inequality by using the obtained solutions.

$$\frac{1}{4}\left(x-2\right)^{2}\leq 0$$

Inequality holds for x=2.

$$x=2$$