Solve sqrt{5}=2.236text{evaluate}frac{3-sqrt{5}}{3+2sqrt{5}}

$$\sqrt { 5 } = 2.236 \text { evaluate } \frac { 3 - \sqrt { 5 } } { 3 + 2 \sqrt { 5 } }$$

Solve for l

$$l=\frac{125\left(19\sqrt{5}+45\right)}{1118tuv\left(ea\right)^{2}}$$

$$a\neq 0\text{ and }t\neq 0\text{ and }u\neq 0\text{ and }v\neq 0$$

Steps for Solving Linear Equation

Multiply e and e to get e^{2}.

$$\sqrt{5}=2.236e^{2}valuat\times \frac{3-\sqrt{5}}{3+2\sqrt{5}}$$

Multiply a and a to get a^{2}.

$$\sqrt{5}=2.236e^{2}va^{2}lut\times \frac{3-\sqrt{5}}{3+2\sqrt{5}}$$

Rationalize the denominator of \frac{3-\sqrt{5}}{3+2\sqrt{5}} by multiplying numerator and denominator by 3-2\sqrt{5}.

$$\sqrt{5}=2.236e^{2}va^{2}lut\times \frac{\left(3-\sqrt{5}\right)\left(3-2\sqrt{5}\right)}{\left(3+2\sqrt{5}\right)\left(3-2\sqrt{5}\right)}$$

Consider \left(3+2\sqrt{5}\right)\left(3-2\sqrt{5}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\sqrt{5}=2.236e^{2}va^{2}lut\times \frac{\left(3-\sqrt{5}\right)\left(3-2\sqrt{5}\right)}{3^{2}-\left(2\sqrt{5}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{5}=2.236e^{2}va^{2}lut\times \frac{\left(3-\sqrt{5}\right)\left(3-2\sqrt{5}\right)}{9-\left(2\sqrt{5}\right)^{2}}$$

Expand \left(2\sqrt{5}\right)^{2}.

$$\sqrt{5}=2.236e^{2}va^{2}lut\times \frac{\left(3-\sqrt{5}\right)\left(3-2\sqrt{5}\right)}{9-2^{2}\left(\sqrt{5}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{5}=2.236e^{2}va^{2}lut\times \frac{\left(3-\sqrt{5}\right)\left(3-2\sqrt{5}\right)}{9-4\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\sqrt{5}=2.236e^{2}va^{2}lut\times \frac{\left(3-\sqrt{5}\right)\left(3-2\sqrt{5}\right)}{9-4\times 5}$$

Multiply 4 and 5 to get 20.

$$\sqrt{5}=2.236e^{2}va^{2}lut\times \frac{\left(3-\sqrt{5}\right)\left(3-2\sqrt{5}\right)}{9-20}$$

Subtract 20 from 9 to get -11.

$$\sqrt{5}=2.236e^{2}va^{2}lut\times \frac{\left(3-\sqrt{5}\right)\left(3-2\sqrt{5}\right)}{-11}$$

Express e^{2}\times \frac{\left(3-\sqrt{5}\right)\left(3-2\sqrt{5}\right)}{-11} as a single fraction.

$$\sqrt{5}=2.236\times \frac{e^{2}\left(3-\sqrt{5}\right)\left(3-2\sqrt{5}\right)}{-11}va^{2}lut$$

Use the distributive property to multiply e^{2} by 3-\sqrt{5}.

$$\sqrt{5}=2.236\times \frac{\left(3e^{2}-e^{2}\sqrt{5}\right)\left(3-2\sqrt{5}\right)}{-11}va^{2}lut$$

Use the distributive property to multiply 3e^{2}-e^{2}\sqrt{5} by 3-2\sqrt{5} and combine like terms.

$$\sqrt{5}=2.236\times \frac{9e^{2}-9e^{2}\sqrt{5}+2e^{2}\left(\sqrt{5}\right)^{2}}{-11}va^{2}lut$$

The square of \sqrt{5} is 5.

$$\sqrt{5}=2.236\times \frac{9e^{2}-9e^{2}\sqrt{5}+2e^{2}\times 5}{-11}va^{2}lut$$

Multiply 2 and 5 to get 10.

$$\sqrt{5}=2.236\times \frac{9e^{2}-9e^{2}\sqrt{5}+10e^{2}}{-11}va^{2}lut$$

Combine 9e^{2} and 10e^{2} to get 19e^{2}.

$$\sqrt{5}=2.236\times \frac{19e^{2}-9e^{2}\sqrt{5}}{-11}va^{2}lut$$

Express \frac{19e^{2}-9e^{2}\sqrt{5}}{-11}v as a single fraction.

$$\sqrt{5}=2.236\times \frac{\left(19e^{2}-9e^{2}\sqrt{5}\right)v}{-11}a^{2}lut$$

Express \frac{\left(19e^{2}-9e^{2}\sqrt{5}\right)v}{-11}a^{2} as a single fraction.

$$\sqrt{5}=2.236\times \frac{\left(19e^{2}-9e^{2}\sqrt{5}\right)va^{2}}{-11}lut$$

Express \frac{\left(19e^{2}-9e^{2}\sqrt{5}\right)va^{2}}{-11}l as a single fraction.

$$\sqrt{5}=2.236\times \frac{\left(19e^{2}-9e^{2}\sqrt{5}\right)va^{2}l}{-11}ut$$

Express \frac{\left(19e^{2}-9e^{2}\sqrt{5}\right)va^{2}l}{-11}u as a single fraction.

$$\sqrt{5}=2.236\times \frac{\left(19e^{2}-9e^{2}\sqrt{5}\right)va^{2}lu}{-11}t$$

Express \frac{\left(19e^{2}-9e^{2}\sqrt{5}\right)va^{2}lu}{-11}t as a single fraction.

$$\sqrt{5}=2.236\times \frac{\left(19e^{2}-9e^{2}\sqrt{5}\right)va^{2}lut}{-11}$$

Multiply both sides of the equation by -11.

$$-11\sqrt{5}=2.236\left(19e^{2}-9e^{2}\sqrt{5}\right)va^{2}lut$$

Reorder the terms.

$$-11\sqrt{5}=2.236\left(-9\sqrt{5}e^{2}+19e^{2}\right)ltuva^{2}$$

Use the distributive property to multiply 2.236 by -9\sqrt{5}e^{2}+19e^{2}.

$$-11\sqrt{5}=\left(-20.124e^{2}\sqrt{5}+42.484e^{2}\right)ltuva^{2}$$

Use the distributive property to multiply -20.124e^{2}\sqrt{5}+42.484e^{2} by l.

$$-11\sqrt{5}=\left(-20.124e^{2}\sqrt{5}l+42.484e^{2}l\right)tuva^{2}$$

Use the distributive property to multiply -20.124e^{2}\sqrt{5}l+42.484e^{2}l by t.

$$-11\sqrt{5}=\left(-20.124e^{2}\sqrt{5}lt+42.484e^{2}lt\right)uva^{2}$$

Use the distributive property to multiply -20.124e^{2}\sqrt{5}lt+42.484e^{2}lt by u.

$$-11\sqrt{5}=\left(-20.124e^{2}\sqrt{5}ltu+42.484e^{2}ltu\right)va^{2}$$

Use the distributive property to multiply -20.124e^{2}\sqrt{5}ltu+42.484e^{2}ltu by v.

$$-11\sqrt{5}=\left(-20.124e^{2}\sqrt{5}ltuv+42.484e^{2}ltuv\right)a^{2}$$

Use the distributive property to multiply -20.124e^{2}\sqrt{5}ltuv+42.484e^{2}ltuv by a^{2}.

$$-11\sqrt{5}=-20.124e^{2}\sqrt{5}ltuva^{2}+42.484e^{2}ltuva^{2}$$

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

$$-20.124e^{2}\sqrt{5}ltuva^{2}+42.484e^{2}ltuva^{2}=-11\sqrt{5}$$

Combine all terms containing l.

$$\left(-20.124e^{2}\sqrt{5}tuva^{2}+42.484e^{2}tuva^{2}\right)l=-11\sqrt{5}$$

The equation is in standard form.

$$\frac{-5031\sqrt{5}e^{2}tuva^{2}+10621e^{2}tuva^{2}}{250}l=-11\sqrt{5}$$

Divide both sides by -20.124e^{2}\sqrt{5}tuva^{2}+42.484e^{2}tuva^{2}.

$$\frac{250\times \frac{-5031\sqrt{5}e^{2}tuva^{2}+10621e^{2}tuva^{2}}{250}l}{-5031\sqrt{5}e^{2}tuva^{2}+10621e^{2}tuva^{2}}=\frac{250\left(-11\sqrt{5}\right)}{-5031\sqrt{5}e^{2}tuva^{2}+10621e^{2}tuva^{2}}$$

Dividing by -20.124e^{2}\sqrt{5}tuva^{2}+42.484e^{2}tuva^{2} undoes the multiplication by -20.124e^{2}\sqrt{5}tuva^{2}+42.484e^{2}tuva^{2}.

$$l=\frac{250\left(-11\sqrt{5}\right)}{-5031\sqrt{5}e^{2}tuva^{2}+10621e^{2}tuva^{2}}$$

Divide -11\sqrt{5} by -20.124e^{2}\sqrt{5}tuva^{2}+42.484e^{2}tuva^{2}.

$$l=\frac{15625\left(\frac{10621\sqrt{5}}{250}+100.62\right)}{312481tuv\left(ea\right)^{2}}$$

Solve for a (complex solution)

$$a=-\frac{5\sqrt{106210\sqrt{5}+251550}l^{-0.5}t^{-0.5}u^{-0.5}v^{-0.5}}{1118e}$$

$$a=\frac{5\sqrt{106210\sqrt{5}+251550}l^{-0.5}t^{-0.5}u^{-0.5}v^{-0.5}}{1118e}\text{, }t\neq 0\text{ and }u\neq 0\text{ and }l\neq 0\text{ and }v\neq 0$$