Solve 2=-5*12+11+11*3+a/sqrt{12^2+11^2+1}

$$2 = \frac{ -5 \times 12+11+11 \times 3+a }{ \sqrt{ { 12 }^{ 2 } + { 11 }^{ 2 } +1 } }$$

Solve for a

$$a=2\left(\sqrt{266}+8\right)\approx 48.619012861$$

Steps for Solving Linear Equation

Multiply -5 and 12 to get -60. Multiply 11 and 3 to get 33.

$$2=\frac{-60+11+33+a}{\sqrt{12^{2}+11^{2}+1}}$$

Add -60 and 11 to get -49.

$$2=\frac{-49+33+a}{\sqrt{12^{2}+11^{2}+1}}$$

Add -49 and 33 to get -16.

$$2=\frac{-16+a}{\sqrt{12^{2}+11^{2}+1}}$$

Calculate 12 to the power of 2 and get 144.

$$2=\frac{-16+a}{\sqrt{144+11^{2}+1}}$$

Calculate 11 to the power of 2 and get 121.

$$2=\frac{-16+a}{\sqrt{144+121+1}}$$

Add 144 and 121 to get 265.

$$2=\frac{-16+a}{\sqrt{265+1}}$$

Add 265 and 1 to get 266.

$$2=\frac{-16+a}{\sqrt{266}}$$

Rationalize the denominator of \frac{-16+a}{\sqrt{266}} by multiplying numerator and denominator by \sqrt{266}.

$$2=\frac{\left(-16+a\right)\sqrt{266}}{\left(\sqrt{266}\right)^{2}}$$

The square of \sqrt{266} is 266.

$$2=\frac{\left(-16+a\right)\sqrt{266}}{266}$$

Use the distributive property to multiply -16+a by \sqrt{266}.

$$2=\frac{-16\sqrt{266}+a\sqrt{266}}{266}$$

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

$$\frac{-16\sqrt{266}+a\sqrt{266}}{266}=2$$

Multiply both sides by 266.

$$-16\sqrt{266}+a\sqrt{266}=2\times 266$$

Multiply 2 and 266 to get 532.

$$-16\sqrt{266}+a\sqrt{266}=532$$

Add 16\sqrt{266} to both sides.

$$a\sqrt{266}=532+16\sqrt{266}$$

The equation is in standard form.

$$\sqrt{266}a=16\sqrt{266}+532$$

Divide both sides by \sqrt{266}.

$$\frac{\sqrt{266}a}{\sqrt{266}}=\frac{16\sqrt{266}+532}{\sqrt{266}}$$

Dividing by \sqrt{266} undoes the multiplication by \sqrt{266}.

$$a=\frac{16\sqrt{266}+532}{\sqrt{266}}$$

Divide 532+16\sqrt{266} by \sqrt{266}.

$$a=2\sqrt{266}+16$$