Solve (x+3)^2leq0

$$( x + 3 ) ^ { 2 } \leq 0$$

Solve for x

$$x=-3$$

Solution Steps

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.

$$\left(x+3\right)^{2}=0$$

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, 6 for b, and 9 for c in the quadratic formula.

$$x=\frac{-6±\sqrt{6^{2}-4\times 1\times 9}}{2}$$

Do the calculations.

$$x=\frac{-6±0}{2}$$

Solutions are the same.

$$x=-3$$

Rewrite the inequality by using the obtained solutions.

$$\left(x+3\right)^{2}\leq 0$$

Inequality holds for x=-3.

$$x=-3$$