Solve 5^7-5^9=x^2

$$5 ^ { 7 } - 5 ^ { 9 } = x ^ { 2 }$$

Solve for x (complex solution)

$$x=-250\sqrt{30}i\approx -0-1369.306393763i$$

$$x=250\sqrt{30}i\approx 1369.306393763i$$

Steps by Finding Square Root

Calculate 5 to the power of 7 and get 78125.

$$78125-5^{9}=x^{2}$$

Calculate 5 to the power of 9 and get 1953125.

$$78125-1953125=x^{2}$$

Subtract 1953125 from 78125 to get -1875000.

$$-1875000=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=-1875000$$

The equation is now solved.

$$x=250\sqrt{30}i x=-250\sqrt{30}i$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 7 and get 78125.

$$78125-5^{9}=x^{2}$$

Calculate 5 to the power of 9 and get 1953125.

$$78125-1953125=x^{2}$$

Subtract 1953125 from 78125 to get -1875000.

$$-1875000=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=-1875000$$

Add 1875000 to both sides.

$$x^{2}+1875000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 1875000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1875000}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1875000}}{2}$$

Multiply -4 times 1875000.

$$x=\frac{0±\sqrt{-7500000}}{2}$$

Take the square root of -7500000.

$$x=\frac{0±500\sqrt{30}i}{2}$$

Now solve the equation x=\frac{0±500\sqrt{30}i}{2} when ± is plus.

$$x=250\sqrt{30}i$$

Now solve the equation x=\frac{0±500\sqrt{30}i}{2} when ± is minus.

$$x=-250\sqrt{30}i$$

The equation is now solved.

$$x=250\sqrt{30}i x=-250\sqrt{30}i$$