Solve x^2-8x^2-9=0

$$x ^ { 2 } - 8 x ^ { 2 } - 9 = 0$$

Solve for x (complex solution)

$$x=-\frac{3\sqrt{7}i}{7}\approx -0-1.133893419i$$

$$x=\frac{3\sqrt{7}i}{7}\approx 1.133893419i$$

Steps by Finding Square Root

Combine x^{2} and -8x^{2} to get -7x^{2}.

$$-7x^{2}-9=0$$

Add 9 to both sides. Anything plus zero gives itself.

$$-7x^{2}=9$$

Divide both sides by -7.

$$x^{2}=-\frac{9}{7}$$

The equation is now solved.

$$x=\frac{3\sqrt{7}i}{7} x=-\frac{3\sqrt{7}i}{7}$$

Steps Using the Quadratic Formula

Combine x^{2} and -8x^{2} to get -7x^{2}.

$$-7x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -7 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-7\right)\left(-9\right)}}{2\left(-7\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-7\right)\left(-9\right)}}{2\left(-7\right)}$$

Multiply -4 times -7.

$$x=\frac{0±\sqrt{28\left(-9\right)}}{2\left(-7\right)}$$

Multiply 28 times -9.

$$x=\frac{0±\sqrt{-252}}{2\left(-7\right)}$$

Take the square root of -252.

$$x=\frac{0±6\sqrt{7}i}{2\left(-7\right)}$$

Multiply 2 times -7.

$$x=\frac{0±6\sqrt{7}i}{-14}$$

Now solve the equation x=\frac{0±6\sqrt{7}i}{-14} when ± is plus.

$$x=-\frac{3\sqrt{7}i}{7}$$

Now solve the equation x=\frac{0±6\sqrt{7}i}{-14} when ± is minus.

$$x=\frac{3\sqrt{7}i}{7}$$

The equation is now solved.

$$x=-\frac{3\sqrt{7}i}{7} x=\frac{3\sqrt{7}i}{7}$$