Solve (x-2*4)^2+3*6^2=x^2

$$( x - 2 \cdot 4 ) ^ { 2 } + 3 \cdot 6 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x = \frac{43}{4} = 10\frac{3}{4} = 10.75$$

Steps for Solving Linear Equation

Multiply 2 and 4 to get 8.

$$\left(x-8\right)^{2}+3\times 6^{2}=x^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-8\right)^{2}.

$$x^{2}-16x+64+3\times 6^{2}=x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}-16x+64+3\times 36=x^{2}$$

Multiply 3 and 36 to get 108.

$$x^{2}-16x+64+108=x^{2}$$

Add 64 and 108 to get 172.

$$x^{2}-16x+172=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-16x+172-x^{2}=0$$

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

$$-16x+172=0$$

Subtract 172 from both sides. Anything subtracted from zero gives its negation.

$$-16x=-172$$

Divide both sides by -16.

$$x=\frac{-172}{-16}$$

Reduce the fraction \frac{-172}{-16} to lowest terms by extracting and canceling out -4.

$$x=\frac{43}{4}$$