Solve c^2-a^2/bc=frac{10^2+10^2-frac{sqrt{3}}{2}}{200}

$$\frac { c ^ { 2 } - a ^ { 2 } } { b c } = \frac { 10 ^ { 2 } + 10 ^ { 2 } - \frac { \sqrt { 3 } } { 2 } } { 200 }$$

Solve for b (complex solution)

$$b=\frac{400\left(\sqrt{3}+400\right)\left(c^{2}-a^{2}\right)}{159997c}$$

$$c\neq a\text{ and }c\neq 0\text{ and }c\neq -a$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 200bc, the least common multiple of bc,200.

$$200\left(c^{2}-a^{2}\right)=bc\left(10^{2}+10^{2}-\frac{\sqrt{3}}{2}\right)$$

Use the distributive property to multiply 200 by c^{2}-a^{2}.

$$200c^{2}-200a^{2}=bc\left(10^{2}+10^{2}-\frac{\sqrt{3}}{2}\right)$$

Calculate 10 to the power of 2 and get 100.

$$200c^{2}-200a^{2}=bc\left(100+10^{2}-\frac{\sqrt{3}}{2}\right)$$

Calculate 10 to the power of 2 and get 100.

$$200c^{2}-200a^{2}=bc\left(100+100-\frac{\sqrt{3}}{2}\right)$$

Add 100 and 100 to get 200.

$$200c^{2}-200a^{2}=bc\left(200-\frac{\sqrt{3}}{2}\right)$$

Use the distributive property to multiply bc by 200-\frac{\sqrt{3}}{2}.

$$200c^{2}-200a^{2}=200bc+bc\left(-\frac{\sqrt{3}}{2}\right)$$

Express b\left(-\frac{\sqrt{3}}{2}\right) as a single fraction.

$$200c^{2}-200a^{2}=200bc+\frac{-b\sqrt{3}}{2}c$$

Express \frac{-b\sqrt{3}}{2}c as a single fraction.

$$200c^{2}-200a^{2}=200bc+\frac{-b\sqrt{3}c}{2}$$

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

$$200bc+\frac{-b\sqrt{3}c}{2}=200c^{2}-200a^{2}$$

Multiply both sides of the equation by 2.

$$400bc-b\sqrt{3}c=400c^{2}-400a^{2}$$

Combine all terms containing b.

$$\left(400c-\sqrt{3}c\right)b=400c^{2}-400a^{2}$$

The equation is in standard form.

$$\left(-\sqrt{3}c+400c\right)b=400c^{2}-400a^{2}$$

Divide both sides by 400c-\sqrt{3}c.

$$\frac{\left(-\sqrt{3}c+400c\right)b}{-\sqrt{3}c+400c}=\frac{400\left(c-a\right)\left(a+c\right)}{-\sqrt{3}c+400c}$$

Dividing by 400c-\sqrt{3}c undoes the multiplication by 400c-\sqrt{3}c.

$$b=\frac{400\left(c-a\right)\left(a+c\right)}{-\sqrt{3}c+400c}$$

Divide 400\left(a+c\right)\left(-a+c\right) by 400c-\sqrt{3}c.

$$b=\frac{400\left(\sqrt{3}+400\right)\left(c-a\right)\left(a+c\right)}{159997c}$$

Variable b cannot be equal to 0.

$$b=\frac{400\left(\sqrt{3}+400\right)\left(c-a\right)\left(a+c\right)}{159997c}\text{, }b\neq 0$$

Solve for b

$$b=\frac{400\left(\sqrt{3}+400\right)\left(c^{2}-a^{2}\right)}{159997c}$$

$$c\neq 0\text{ and }|c|\neq |a|$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 200bc, the least common multiple of bc,200.

$$200\left(c^{2}-a^{2}\right)=bc\left(10^{2}+10^{2}-\frac{\sqrt{3}}{2}\right)$$

Use the distributive property to multiply 200 by c^{2}-a^{2}.

$$200c^{2}-200a^{2}=bc\left(10^{2}+10^{2}-\frac{\sqrt{3}}{2}\right)$$

Calculate 10 to the power of 2 and get 100.

$$200c^{2}-200a^{2}=bc\left(100+10^{2}-\frac{\sqrt{3}}{2}\right)$$

Calculate 10 to the power of 2 and get 100.

$$200c^{2}-200a^{2}=bc\left(100+100-\frac{\sqrt{3}}{2}\right)$$

Add 100 and 100 to get 200.

$$200c^{2}-200a^{2}=bc\left(200-\frac{\sqrt{3}}{2}\right)$$

Use the distributive property to multiply bc by 200-\frac{\sqrt{3}}{2}.

$$200c^{2}-200a^{2}=200bc+bc\left(-\frac{\sqrt{3}}{2}\right)$$

Express b\left(-\frac{\sqrt{3}}{2}\right) as a single fraction.

$$200c^{2}-200a^{2}=200bc+\frac{-b\sqrt{3}}{2}c$$

Express \frac{-b\sqrt{3}}{2}c as a single fraction.

$$200c^{2}-200a^{2}=200bc+\frac{-b\sqrt{3}c}{2}$$

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

$$200bc+\frac{-b\sqrt{3}c}{2}=200c^{2}-200a^{2}$$

Multiply both sides of the equation by 2.

$$400bc-b\sqrt{3}c=400c^{2}-400a^{2}$$

Combine all terms containing b.

$$\left(400c-\sqrt{3}c\right)b=400c^{2}-400a^{2}$$

The equation is in standard form.

$$\left(-\sqrt{3}c+400c\right)b=400c^{2}-400a^{2}$$

Divide both sides by 400c-\sqrt{3}c.

$$\frac{\left(-\sqrt{3}c+400c\right)b}{-\sqrt{3}c+400c}=\frac{400\left(c-a\right)\left(a+c\right)}{-\sqrt{3}c+400c}$$

Dividing by 400c-\sqrt{3}c undoes the multiplication by 400c-\sqrt{3}c.

$$b=\frac{400\left(c-a\right)\left(a+c\right)}{-\sqrt{3}c+400c}$$

Divide 400\left(a+c\right)\left(-a+c\right) by 400c-\sqrt{3}c.

$$b=\frac{400\left(\sqrt{3}+400\right)\left(c-a\right)\left(a+c\right)}{159997c}$$

Variable b cannot be equal to 0.

$$b=\frac{400\left(\sqrt{3}+400\right)\left(c-a\right)\left(a+c\right)}{159997c}\text{, }b\neq 0$$

Solve for a (complex solution)

$$a=-\frac{\sqrt{c}\sqrt{\sqrt{3}b+400c-400b}}{20}$$

$$a=\frac{\sqrt{c}\sqrt{\sqrt{3}b+400c-400b}}{20}\text{, }b\neq 0\text{ and }c\neq 0$$

Solve for a

$$a=\frac{\sqrt{c\left(\sqrt{3}b+400c-400b\right)}}{20}$$

$$a=-\frac{\sqrt{c\left(\sqrt{3}b+400c-400b\right)}}{20}\text{, }\left(c<0\text{ or }c\geq -\frac{\sqrt{3}b}{400}+b\right)\text{ and }b\neq 0\text{ and }\left(c>0\text{ or }c\leq -\frac{\sqrt{3}b}{400}+b\right)\text{ and }c\neq 0$$