Solve (x-1)^2=(x+4)^2

$$( x - 1 ) ^ { 2 } = ( x + 4 ) ^ { 2 }$$

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

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

$$x^{2}-2x+1=\left(x+4\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$x^{2}-2x+1=x^{2}+8x+16$$

Subtract x^{2} from both sides.

$$x^{2}-2x+1-x^{2}=8x+16$$

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

$$-2x+1=8x+16$$

Subtract 8x from both sides.

$$-2x+1-8x=16$$

Combine -2x and -8x to get -10x.

$$-10x+1=16$$

Subtract 1 from both sides.

$$-10x=16-1$$

Subtract 1 from 16 to get 15.

$$-10x=15$$

Divide both sides by -10.

$$x=\frac{15}{-10}$$

Reduce the fraction \frac{15}{-10} to lowest terms by extracting and canceling out 5.

$$x=-\frac{3}{2}$$