Solve 194^2+left(x-1160right)^2=left(1354-xright)^2

$${ 194 }^{ 2 } + { \left(x-1160 \right) }^{ 2 } = { \left(1354-x \right) }^{ 2 }$$

Solve for x

$$x=1160$$

Steps for Solving Linear Equation

Calculate 194 to the power of 2 and get 37636.

$$37636+\left(x-1160\right)^{2}=\left(1354-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1160\right)^{2}.

$$37636+x^{2}-2320x+1345600=\left(1354-x\right)^{2}$$

Add 37636 and 1345600 to get 1383236.

$$1383236+x^{2}-2320x=\left(1354-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1354-x\right)^{2}.

$$1383236+x^{2}-2320x=1833316-2708x+x^{2}$$

Add 2708x to both sides.

$$1383236+x^{2}-2320x+2708x=1833316+x^{2}$$

Combine -2320x and 2708x to get 388x.

$$1383236+x^{2}+388x=1833316+x^{2}$$

Subtract x^{2} from both sides.

$$1383236+x^{2}+388x-x^{2}=1833316$$

Combine x^{2} and -x^{2} to get 0.

$$1383236+388x=1833316$$

Subtract 1383236 from both sides.

$$388x=1833316-1383236$$

Subtract 1383236 from 1833316 to get 450080.

$$388x=450080$$

Divide both sides by 388.

$$x=\frac{450080}{388}$$

Divide 450080 by 388 to get 1160.

$$x=1160$$