Solve (2sqrt{b1})^2-x^2=2(13^2-x^2)

$$( 2 \sqrt { b 1 } ) ^ { 2 } - x ^ { 2 } = 2 ( 13 ^ { 2 } - x ^ { 2 } )$$

Solve for b_1 (complex solution)

$$b_{1}=-\frac{x^{2}}{4}+\frac{169}{2}$$

Steps for Solving Linear Equation

Expand \left(2\sqrt{b_{1}}\right)^{2}.

$$2^{2}\left(\sqrt{b_{1}}\right)^{2}-x^{2}=2\left(13^{2}-x^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{b_{1}}\right)^{2}-x^{2}=2\left(13^{2}-x^{2}\right)$$

Calculate \sqrt{b_{1}} to the power of 2 and get b_{1}.

$$4b_{1}-x^{2}=2\left(13^{2}-x^{2}\right)$$

Calculate 13 to the power of 2 and get 169.

$$4b_{1}-x^{2}=2\left(169-x^{2}\right)$$

Use the distributive property to multiply 2 by 169-x^{2}.

$$4b_{1}-x^{2}=338-2x^{2}$$

Add x^{2} to both sides.

$$4b_{1}=338-2x^{2}+x^{2}$$

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

$$4b_{1}=338-x^{2}$$

Divide both sides by 4.

$$\frac{4b_{1}}{4}=\frac{338-x^{2}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$b_{1}=\frac{338-x^{2}}{4}$$

Divide 338-x^{2} by 4.

$$b_{1}=-\frac{x^{2}}{4}+\frac{169}{2}$$

Solve for b_1

$$b_{1}=-\frac{x^{2}}{4}+\frac{169}{2}$$

$$|x|\leq 13\sqrt{2}$$

Steps for Solving Linear Equation

Expand \left(2\sqrt{b_{1}}\right)^{2}.

$$2^{2}\left(\sqrt{b_{1}}\right)^{2}-x^{2}=2\left(13^{2}-x^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{b_{1}}\right)^{2}-x^{2}=2\left(13^{2}-x^{2}\right)$$

Calculate \sqrt{b_{1}} to the power of 2 and get b_{1}.

$$4b_{1}-x^{2}=2\left(13^{2}-x^{2}\right)$$

Calculate 13 to the power of 2 and get 169.

$$4b_{1}-x^{2}=2\left(169-x^{2}\right)$$

Use the distributive property to multiply 2 by 169-x^{2}.

$$4b_{1}-x^{2}=338-2x^{2}$$

Add x^{2} to both sides.

$$4b_{1}=338-2x^{2}+x^{2}$$

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

$$4b_{1}=338-x^{2}$$

Divide both sides by 4.

$$\frac{4b_{1}}{4}=\frac{338-x^{2}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$b_{1}=\frac{338-x^{2}}{4}$$

Divide 338-x^{2} by 4.

$$b_{1}=-\frac{x^{2}}{4}+\frac{169}{2}$$

Solve for x (complex solution)

$$x=-\sqrt{338-4b_{1}}$$

$$x=\sqrt{338-4b_{1}}$$

Solve for x

$$x=\sqrt{338-4b_{1}}$$

$$x=-\sqrt{338-4b_{1}}\text{, }b_{1}\geq 0\text{ and }b_{1}\leq \frac{169}{2}$$