Solve 4a^2+4a+1>0

$$4 a ^ { 2 } + 4 a + 1 > 0$$

Solve for a

$$a\neq -\frac{1}{2}$$

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.

$$4a^{2}+4a+1=0$$

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.

$$a=\frac{-4±\sqrt{4^{2}-4\times 4\times 1}}{2\times 4}$$

Do the calculations.

$$a=\frac{-4±0}{8}$$

Solutions are the same.

$$a=-\frac{1}{2}$$

Rewrite the inequality by using the obtained solutions.

$$4\left(a+\frac{1}{2}\right)^{2}>0$$

Inequality holds for a\neq -\frac{1}{2}.

$$a\neq -\frac{1}{2}$$