Solve x^2+1738^2=1838^2

$$x ^ { 2 } + 1738 ^ { 2 } = 1838 ^ { 2 }$$

Solve for x

$$x=20\sqrt{894}\approx 597.996655509$$

$$x=-20\sqrt{894}\approx -597.996655509$$

Steps by Finding Square Root

Calculate 1738 to the power of 2 and get 3020644.

$$x^{2}+3020644=1838^{2}$$

Calculate 1838 to the power of 2 and get 3378244.

$$x^{2}+3020644=3378244$$

Subtract 3020644 from both sides.

$$x^{2}=3378244-3020644$$

Subtract 3020644 from 3378244 to get 357600.

$$x^{2}=357600$$

Take the square root of both sides of the equation.

$$x=20\sqrt{894} x=-20\sqrt{894}$$

Steps Using the Quadratic Formula

Calculate 1738 to the power of 2 and get 3020644.

$$x^{2}+3020644=1838^{2}$$

Calculate 1838 to the power of 2 and get 3378244.

$$x^{2}+3020644=3378244$$

Subtract 3378244 from both sides.

$$x^{2}[phone]=0$$

Subtract 3378244 from 3020644 to get -357600.

$$x^{2}-357600=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -357600 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-357600\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-357600\right)}}{2}$$

Multiply -4 times -357600.

$$x=\frac{0±\sqrt{1430400}}{2}$$

Take the square root of 1430400.

$$x=\frac{0±40\sqrt{894}}{2}$$

Now solve the equation x=\frac{0±40\sqrt{894}}{2} when ± is plus.

$$x=20\sqrt{894}$$

Now solve the equation x=\frac{0±40\sqrt{894}}{2} when ± is minus.

$$x=-20\sqrt{894}$$

The equation is now solved.

$$x=20\sqrt{894} x=-20\sqrt{894}$$