Solve (4+x)^2=16+Delta+x^2

$$( 4 + x ) ^ { 2 } = 16 + \Delta + x ^ { 2 }$$

Solve for x

$$x=\frac{\Delta }{8}$$

Steps for Solving Linear Equation

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

$$16+8x+x^{2}=16+\Delta +x^{2}$$

Subtract x^{2} from both sides.

$$16+8x+x^{2}-x^{2}=16+\Delta$$

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

$$16+8x=16+\Delta$$

Subtract 16 from both sides.

$$8x=16+\Delta -16$$

Subtract 16 from 16 to get 0.

$$8x=\Delta$$

Divide both sides by 8.

$$\frac{8x}{8}=\frac{\Delta }{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{\Delta }{8}$$

Solve for Δ

$$\Delta =8x$$

Solution Steps

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

$$16+8x+x^{2}=16+\Delta +x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$16+\Delta +x^{2}=16+8x+x^{2}$$

Subtract 16 from both sides.

$$\Delta +x^{2}=16+8x+x^{2}-16$$

Subtract 16 from 16 to get 0.

$$\Delta +x^{2}=8x+x^{2}$$

Subtract x^{2} from both sides.

$$\Delta =8x+x^{2}-x^{2}$$

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

$$\Delta =8x$$