Solve 10^2=(2x)^2+(1+y)

$$10 ^ { 2 } = ( 2 x ) ^ { 2 } + ( 1 + y )$$

Solve for y

$$y=99-4x^{2}$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$100=\left(2x\right)^{2}+1+y$$

Expand \left(2x\right)^{2}.

$$100=2^{2}x^{2}+1+y$$

Calculate 2 to the power of 2 and get 4.

$$100=4x^{2}+1+y$$

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

$$4x^{2}+1+y=100$$

Subtract 4x^{2} from both sides.

$$1+y=100-4x^{2}$$

Subtract 1 from both sides.

$$y=100-4x^{2}-1$$

Subtract 1 from 100 to get 99.

$$y=99-4x^{2}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{99-y}}{2}$$

$$x=\frac{\sqrt{99-y}}{2}$$

Solve for x

$$x=\frac{\sqrt{99-y}}{2}$$

$$x=-\frac{\sqrt{99-y}}{2}\text{, }y\leq 99$$