Solve (x-3)^2+4^2=x^2

$$( x - 3 ) ^ { 2 } + 4 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x = \frac{25}{6} = 4\frac{1}{6} \approx 4.166666667$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-6x+9+4^{2}=x^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}-6x+9+16=x^{2}$$

Add 9 and 16 to get 25.

$$x^{2}-6x+25=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-6x+25-x^{2}=0$$

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

$$-6x+25=0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$-6x=-25$$

Divide both sides by -6.

$$x=\frac{-25}{-6}$$

Fraction \frac{-25}{-6} can be simplified to \frac{25}{6} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{25}{6}$$