Solve left(x+6right)^2=left(4+xright)^2+4sqrt{2}*4sqrt{2}

$${ \left(x+6 \right) }^{ 2 } = { \left(4+x \right) }^{ 2 } +4 \sqrt{ 2 } \times 4 \sqrt{ 2 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\left(x+6\right)^{2}=\left(4+x\right)^{2}+4\times 4\times 2$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$x^{2}+12x+36=\left(4+x\right)^{2}+4\times 4\times 2$$

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

$$x^{2}+12x+36=16+8x+x^{2}+4\times 4\times 2$$

Multiply 4 and 4 to get 16.

$$x^{2}+12x+36=16+8x+x^{2}+16\times 2$$

Multiply 16 and 2 to get 32.

$$x^{2}+12x+36=16+8x+x^{2}+32$$

Add 16 and 32 to get 48.

$$x^{2}+12x+36=48+8x+x^{2}$$

Subtract 8x from both sides.

$$x^{2}+12x+36-8x=48+x^{2}$$

Combine 12x and -8x to get 4x.

$$x^{2}+4x+36=48+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+4x+36-x^{2}=48$$

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

$$4x+36=48$$

Subtract 36 from both sides.

$$4x=48-36$$

Subtract 36 from 48 to get 12.

$$4x=12$$

Divide both sides by 4.

$$x=\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$x=3$$