Solve 2^frac{pi{2}}k+59=2*2^3-3*3^2+k*2+18*3+1

$$2 ^ { \frac { \pi } { 2 } } k + 59 = 2 \cdot 2 ^ { 3 } - 3 \cdot 3 ^ { 2 } + k \cdot 2 + 18 \cdot 3 + 1$$

Solve for k

$$k = -\frac{15}{2 ^ {\frac{\pi}{2}} - 2} \approx -15.452982174$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$2^{\frac{\pi }{2}}k+59=2^{4}-3\times 3^{2}+k\times 2+18\times 3+1$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$2^{\frac{\pi }{2}}k+59=2^{4}-3^{3}+k\times 2+18\times 3+1$$

Calculate 2 to the power of 4 and get 16.

$$2^{\frac{\pi }{2}}k+59=16-3^{3}+k\times 2+18\times 3+1$$

Calculate 3 to the power of 3 and get 27.

$$2^{\frac{\pi }{2}}k+59=16-27+k\times 2+18\times 3+1$$

Subtract 27 from 16 to get -11.

$$2^{\frac{\pi }{2}}k+59=-11+k\times 2+18\times 3+1$$

Multiply 18 and 3 to get 54.

$$2^{\frac{\pi }{2}}k+59=-11+k\times 2+54+1$$

Add -11 and 54 to get 43.

$$2^{\frac{\pi }{2}}k+59=43+k\times 2+1$$

Add 43 and 1 to get 44.

$$2^{\frac{\pi }{2}}k+59=44+k\times 2$$

Subtract k\times 2 from both sides.

$$2^{\frac{\pi }{2}}k+59-k\times 2=44$$

Multiply -1 and 2 to get -2.

$$2^{\frac{\pi }{2}}k+59-2k=44$$

Subtract 59 from both sides.

$$2^{\frac{\pi }{2}}k-2k=44-59$$

Subtract 59 from 44 to get -15.

$$2^{\frac{\pi }{2}}k-2k=-15$$

Combine all terms containing k.

$$\left(2^{\frac{\pi }{2}}-2\right)k=-15$$

Divide both sides by 2^{\frac{1}{2}\pi }-2.

$$\frac{\left(2^{\frac{\pi }{2}}-2\right)k}{2^{\frac{\pi }{2}}-2}=-\frac{15}{2^{\frac{\pi }{2}}-2}$$

Dividing by 2^{\frac{1}{2}\pi }-2 undoes the multiplication by 2^{\frac{1}{2}\pi }-2.

$$k=-\frac{15}{2^{\frac{\pi }{2}}-2}$$