Solve -(a+2)^2leq0

$$- ( a + 2 ) ^ { 2 } \leq 0$$

Solve for a

$$a\in \mathrm{R}$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(a+2\right)^{2}.

$$-\left(a^{2}+4a+4\right)\leq 0$$

To find the opposite of a^{2}+4a+4, find the opposite of each term.

$$-a^{2}-4a-4\leq 0$$

Multiply the inequality by -1 to make the coefficient of the highest power in -a^{2}-4a-4 positive. Since -1 is negative, the inequality direction is changed.

$$a^{2}+4a+4\geq 0$$

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.

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

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

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

Do the calculations.

$$a=\frac{-4±0}{2}$$

Solutions are the same.

$$a=-2$$

Rewrite the inequality by using the obtained solutions.

$$\left(a+2\right)^{2}\geq 0$$

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

$$a\in \mathrm{R}$$