Solve k+121/sqrt{3^2+4^2}=3

$$\frac { k + 121 } { \sqrt { 3 ^ { 2 } + 4 ^ { 2 } } } = 3$$

Solve for k

$$k=-106$$

Steps for Solving Linear Equation

Calculate 3 to the power of 2 and get 9.

$$\frac{k+121}{\sqrt{9+4^{2}}}=3$$

Calculate 4 to the power of 2 and get 16.

$$\frac{k+121}{\sqrt{9+16}}=3$$

Add 9 and 16 to get 25.

$$\frac{k+121}{\sqrt{25}}=3$$

Calculate the square root of 25 and get 5.

$$\frac{k+121}{5}=3$$

Divide each term of k+121 by 5 to get \frac{1}{5}k+\frac{121}{5}.

$$\frac{1}{5}k+\frac{121}{5}=3$$

Subtract \frac{121}{5} from both sides.

$$\frac{1}{5}k=3-\frac{121}{5}$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{1}{5}k=\frac{15}{5}-\frac{121}{5}$$

Since \frac{15}{5} and \frac{121}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}k=\frac{15-121}{5}$$

Subtract 121 from 15 to get -106.

$$\frac{1}{5}k=-\frac{106}{5}$$

Multiply both sides by 5, the reciprocal of \frac{1}{5}.

$$k=-\frac{106}{5}\times 5$$

Cancel out 5 and 5.

$$k=-106$$