Solve x^2+50^2=6.8^2

$$x ^ { 2 } + 50 ^ { 2 } = 6.8 ^ { 2 }$$

Solve for x (complex solution)

$$x=-\frac{i\times 12\sqrt{426}}{5}\approx -0-49.535441857i$$

$$x=\frac{i\times 12\sqrt{426}}{5}\approx 49.535441857i$$

Steps by Finding Square Root

Calculate 50 to the power of 2 and get 2500.

$$x^{2}+2500=6.8^{2}$$

Calculate 6.8 to the power of 2 and get 46.24.

$$x^{2}+2500=46.24$$

Subtract 2500 from both sides.

$$x^{2}=46.24-2500$$

Subtract 2500 from 46.24 to get -2453.76.

$$x^{2}=-2453.76$$

The equation is now solved.

$$x=\frac{12\sqrt{426}i}{5} x=-\frac{12\sqrt{426}i}{5}$$

Steps Using the Quadratic Formula

Calculate 50 to the power of 2 and get 2500.

$$x^{2}+2500=6.8^{2}$$

Calculate 6.8 to the power of 2 and get 46.24.

$$x^{2}+2500=46.24$$

Subtract 46.24 from both sides.

$$x^{2}+2500-46.24=0$$

Subtract 46.24 from 2500 to get 2453.76.

$$x^{2}+2453.76=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 2453.76 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2453.76}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2453.76}}{2}$$

Multiply -4 times 2453.76.

$$x=\frac{0±\sqrt{-9815.04}}{2}$$

Take the square root of -9815.04.

$$x=\frac{0±\frac{24\sqrt{426}i}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{24\sqrt{426}i}{5}}{2} when ± is plus.

$$x=\frac{12\sqrt{426}i}{5}$$

Now solve the equation x=\frac{0±\frac{24\sqrt{426}i}{5}}{2} when ± is minus.

$$x=-\frac{12\sqrt{426}i}{5}$$

The equation is now solved.

$$x=\frac{12\sqrt{426}i}{5} x=-\frac{12\sqrt{426}i}{5}$$