Solve x^2+18x+81leq0

$$x ^ { 2 } + 18 x + 81 \leq 0$$

Solve for x

$$x=-9$$

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.

$$x^{2}+18x+81=0$$

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, 18 for b, and 81 for c in the quadratic formula.

$$x=\frac{-18±\sqrt{18^{2}-4\times 1\times 81}}{2}$$

Do the calculations.

$$x=\frac{-18±0}{2}$$

Solutions are the same.

$$x=-9$$

Rewrite the inequality by using the obtained solutions.

$$\left(x+9\right)^{2}\leq 0$$

Inequality holds for x=-9.

$$x=-9$$