Solve -x^2-8.8=0

$$- { x }^{ 2 } -8.8=0$$

Solve for x (complex solution)

$$x=-\frac{i\times 2\sqrt{55}}{5}\approx -0-2.966479395i$$

$$x=\frac{i\times 2\sqrt{55}}{5}\approx 2.966479395i$$

Steps by Finding Square Root

Add 8.8 to both sides. Anything plus zero gives itself.

$$-x^{2}=8.8$$

Divide both sides by -1.

$$x^{2}=\frac{8.8}{-1}$$

Expand \frac{8.8}{-1} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{88}{-10}$$

Reduce the fraction \frac{88}{-10} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{44}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{55}i}{5} x=-\frac{2\sqrt{55}i}{5}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-x^{2}-8.8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -8.8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-8.8\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-8.8\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-8.8\right)}}{2\left(-1\right)}$$

Multiply 4 times -8.8.

$$x=\frac{0±\sqrt{-35.2}}{2\left(-1\right)}$$

Take the square root of -35.2.

$$x=\frac{0±\frac{4\sqrt{55}i}{5}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±\frac{4\sqrt{55}i}{5}}{-2}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{55}i}{5}}{-2} when ± is plus.

$$x=-\frac{2\sqrt{55}i}{5}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{55}i}{5}}{-2} when ± is minus.

$$x=\frac{2\sqrt{55}i}{5}$$

The equation is now solved.

$$x=-\frac{2\sqrt{55}i}{5} x=\frac{2\sqrt{55}i}{5}$$