Solve x^2=(250-90)^2/90+(50-210)^2/210=

$$x ^ { 2 } = \frac { ( 250 - 90 ) ^ { 2 } } { 90 } + \frac { ( 50 - 210 ) ^ { 2 } } { 210 } =$$

Solve for x

$$x = \frac{160 \sqrt{7}}{21} \approx 20.158105227$$

$$x = -\frac{160 \sqrt{7}}{21} \approx -20.158105227$$

Steps by Finding Square Root

Multiply both sides of the equation by 630, the least common multiple of 90,210.

$$630x^{2}=7\left(250-90\right)^{2}+3\left(50-210\right)^{2}$$

Subtract 90 from 250 to get 160.

$$630x^{2}=7\times 160^{2}+3\left(50-210\right)^{2}$$

Calculate 160 to the power of 2 and get 25600.

$$630x^{2}=7\times 25600+3\left(50-210\right)^{2}$$

Multiply 7 and 25600 to get 179200.

$$630x^{2}=179200+3\left(50-210\right)^{2}$$

Subtract 210 from 50 to get -160.

$$630x^{2}=179200+3\left(-160\right)^{2}$$

Calculate -160 to the power of 2 and get 25600.

$$630x^{2}=179200+3\times 25600$$

Multiply 3 and 25600 to get 76800.

$$630x^{2}=179200+76800$$

Add 179200 and 76800 to get 256000.

$$630x^{2}=256000$$

Divide both sides by 630.

$$x^{2}=\frac{256000}{630}$$

Reduce the fraction \frac{256000}{630} to lowest terms by extracting and canceling out 10.

$$x^{2}=\frac{25600}{63}$$

Take the square root of both sides of the equation.

$$x=\frac{160\sqrt{7}}{21} x=-\frac{160\sqrt{7}}{21}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 630, the least common multiple of 90,210.

$$630x^{2}=7\left(250-90\right)^{2}+3\left(50-210\right)^{2}$$

Subtract 90 from 250 to get 160.

$$630x^{2}=7\times 160^{2}+3\left(50-210\right)^{2}$$

Calculate 160 to the power of 2 and get 25600.

$$630x^{2}=7\times 25600+3\left(50-210\right)^{2}$$

Multiply 7 and 25600 to get 179200.

$$630x^{2}=179200+3\left(50-210\right)^{2}$$

Subtract 210 from 50 to get -160.

$$630x^{2}=179200+3\left(-160\right)^{2}$$

Calculate -160 to the power of 2 and get 25600.

$$630x^{2}=179200+3\times 25600$$

Multiply 3 and 25600 to get 76800.

$$630x^{2}=179200+76800$$

Add 179200 and 76800 to get 256000.

$$630x^{2}=256000$$

Subtract 256000 from both sides.

$$630x^{2}-256000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 630 for a, 0 for b, and -256000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 630\left(-256000\right)}}{2\times 630}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 630\left(-256000\right)}}{2\times 630}$$

Multiply -4 times 630.

$$x=\frac{0±\sqrt{-2520\left(-256000\right)}}{2\times 630}$$

Multiply -2520 times -256000.

$$x=\frac{0±\sqrt{645120000}}{2\times 630}$$

Take the square root of 645120000.

$$x=\frac{0±9600\sqrt{7}}{2\times 630}$$

Multiply 2 times 630.

$$x=\frac{0±9600\sqrt{7}}{1260}$$

Now solve the equation x=\frac{0±9600\sqrt{7}}{1260} when ± is plus.

$$x=\frac{160\sqrt{7}}{21}$$

Now solve the equation x=\frac{0±9600\sqrt{7}}{1260} when ± is minus.

$$x=-\frac{160\sqrt{7}}{21}$$

The equation is now solved.

$$x=\frac{160\sqrt{7}}{21} x=-\frac{160\sqrt{7}}{21}$$