Solve (a-1)^2=a^2-7a-4

$$( a - 1 ) ^ { 2 } = a ^ { 2 } - 7 a - 4$$

Solve for a

$$a=-1$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(a-1\right)^{2}.

$$a^{2}-2a+1=a^{2}-7a-4$$

Subtract a^{2} from both sides.

$$a^{2}-2a+1-a^{2}=-7a-4$$

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

$$-2a+1=-7a-4$$

Add 7a to both sides.

$$-2a+1+7a=-4$$

Combine -2a and 7a to get 5a.

$$5a+1=-4$$

Subtract 1 from both sides.

$$5a=-4-1$$

Subtract 1 from -4 to get -5.

$$5a=-5$$

Divide both sides by 5.

$$a=\frac{-5}{5}$$

Divide -5 by 5 to get -1.

$$a=-1$$