Solve (x+7)^2-k=3

$$( x + 7 ) ^ { 2 } - k = 3$$

Solve for k

$$k=\left(x+7\right)^{2}-3$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+7\right)^{2}.

$$x^{2}+14x+49-k=3$$

Subtract x^{2} from both sides.

$$14x+49-k=3-x^{2}$$

Subtract 14x from both sides.

$$49-k=3-x^{2}-14x$$

Subtract 49 from both sides.

$$-k=3-x^{2}-14x-49$$

Subtract 49 from 3 to get -46.

$$-k=-46-x^{2}-14x$$

The equation is in standard form.

$$-k=-x^{2}-14x-46$$

Divide both sides by -1.

$$\frac{-k}{-1}=\frac{-x^{2}-14x-46}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$k=\frac{-x^{2}-14x-46}{-1}$$

Divide -46-x^{2}-14x by -1.

$$k=x^{2}+14x+46$$

Solve for x (complex solution)

$$x=-\left(\sqrt{k+3}+7\right)$$

$$x=\sqrt{k+3}-7$$

Solve for x

$$x=-\left(\sqrt{k+3}+7\right)$$

$$x=\sqrt{k+3}-7\text{, }k\geq -3$$