Solve 2{e}^frac{1{4}a}=1/2{e}^frac{1{4}a}a+(-1/2a{e}^frac{1{4}a}+2{e}^frac{1{4}a})

$$2 { e }^{ \frac{ 1 }{ 4 } a } = \frac{ 1 }{ 2 } { e }^{ \frac{ 1 }{ 4 } a } a+(- \frac{ 1 }{ 2 } a { e }^{ \frac{ 1 }{ 4 } a } +2 { e }^{ \frac{ 1 }{ 4 } a } )$$

Solve for a (complex solution)

$$a\in \mathrm{C}$$

Solution Steps

Combine \frac{1}{2}e^{\frac{1}{4}a}a and -\frac{1}{2}ae^{\frac{1}{4}a} to get 0.

$$2e^{\frac{1}{4}a}=2e^{\frac{1}{4}a}$$

Subtract 2e^{\frac{1}{4}a} from both sides.

$$2e^{\frac{1}{4}a}-2e^{\frac{1}{4}a}=0$$

Combine 2e^{\frac{1}{4}a} and -2e^{\frac{1}{4}a} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{C}$$

Solve for a

$$a\in \mathrm{R}$$

Solution Steps

Combine \frac{1}{2}e^{\frac{1}{4}a}a and -\frac{1}{2}ae^{\frac{1}{4}a} to get 0.

$$2e^{\frac{1}{4}a}=2e^{\frac{1}{4}a}$$

Subtract 2e^{\frac{1}{4}a} from both sides.

$$2e^{\frac{1}{4}a}-2e^{\frac{1}{4}a}=0$$

Combine 2e^{\frac{1}{4}a} and -2e^{\frac{1}{4}a} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$