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4x^{2}-4x+1=0
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.
x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 4\times 1}}{2\times 4}
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{4±0}{8}
Do the calculations.
x=\frac{1}{2}
Solutions are the same.
4\left(x-\frac{1}{2}\right)^{2}\leq 0
Rewrite the inequality by using the obtained solutions.
x=\frac{1}{2}
Inequality holds for x=\frac{1}{2}.