Solve 4^1x^2+8a+4=3left(x^1right)^2+3

$${ 4 }^{ 1 } { x }^{ 2 } +8a+4 = 3 { \left( { x }^{ 1 } \right) }^{ 2 } +3$$

Solve for a

$$a=\frac{-x^{2}-1}{8}$$

Steps for Solving Linear Equation

To raise a power to another power, multiply the exponents. Multiply 1 and 2 to get 2.

$$4^{1}x^{2}+8a+4=3x^{2}+3$$

Calculate 4 to the power of 1 and get 4.

$$4x^{2}+8a+4=3x^{2}+3$$

Subtract 4x^{2} from both sides.

$$8a+4=3x^{2}+3-4x^{2}$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$8a+4=-x^{2}+3$$

Subtract 4 from both sides.

$$8a=-x^{2}+3-4$$

Subtract 4 from 3 to get -1.

$$8a=-x^{2}-1$$

Divide both sides by 8.

$$\frac{8a}{8}=\frac{-x^{2}-1}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$a=\frac{-x^{2}-1}{8}$$

Solve for x (complex solution)

$$x=-\sqrt{-8a-1}$$

$$x=\sqrt{-8a-1}$$

Solve for x

$$x=\sqrt{-8a-1}$$

$$x=-\sqrt{-8a-1}\text{, }a\leq -\frac{1}{8}$$