Solve 4x^2-4x+1geq0

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

Solve for x

$$x\in \mathrm{R}$$

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.

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

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 4 for a, -4 for b, and 1 for c in the quadratic formula.

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

Do the calculations.

$$x=\frac{4±0}{8}$$

Solutions are the same.

$$x=\frac{1}{2}$$

Rewrite the inequality by using the obtained solutions.

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

Inequality holds for x\in \mathrm{R}.

$$x\in \mathrm{R}$$