Solve -x^2-10x-25geq0

$$- x ^ { 2 } - 10 x - 25 \geq 0$$

Solve for x

$$x=-5$$

Steps Using the Quadratic Formula

Multiply the inequality by -1 to make the coefficient of the highest power in -x^{2}-10x-25 positive. Since -1 is negative, the inequality direction is changed.

$$x^{2}+10x+25\leq 0$$

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.

$$x^{2}+10x+25=0$$

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, 10 for b, and 25 for c in the quadratic formula.

$$x=\frac{-10±\sqrt{10^{2}-4\times 1\times 25}}{2}$$

Do the calculations.

$$x=\frac{-10±0}{2}$$

Solutions are the same.

$$x=-5$$

Rewrite the inequality by using the obtained solutions.

$$\left(x+5\right)^{2}\leq 0$$

Inequality holds for x=-5.

$$x=-5$$