Solve d=|2*1+6*1+2|/sqrt{1^2+1^2}

$$d = \frac { | 2 \cdot 1 + 6 \cdot 1 + 2 | } { \sqrt { 1 ^ { 2 } + 1 ^ { 2 } } }$$

Solve for d

$$d=5\sqrt{2}\approx 7.071067812$$

Steps for Solving Linear Equation

Multiply 2 and 1 to get 2. Multiply 6 and 1 to get 6.

$$d=\frac{|2+6+2|}{\sqrt{1^{2}+1^{2}}}$$

Add 2 and 6 to get 8.

$$d=\frac{|8+2|}{\sqrt{1^{2}+1^{2}}}$$

Add 8 and 2 to get 10.

$$d=\frac{|10|}{\sqrt{1^{2}+1^{2}}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 10 is 10.

$$d=\frac{10}{\sqrt{1^{2}+1^{2}}}$$

Calculate 1 to the power of 2 and get 1.

$$d=\frac{10}{\sqrt{1+1^{2}}}$$

Calculate 1 to the power of 2 and get 1.

$$d=\frac{10}{\sqrt{1+1}}$$

Add 1 and 1 to get 2.

$$d=\frac{10}{\sqrt{2}}$$

Rationalize the denominator of \frac{10}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$d=\frac{10\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$d=\frac{10\sqrt{2}}{2}$$

Divide 10\sqrt{2} by 2 to get 5\sqrt{2}.

$$d=5\sqrt{2}$$

Assign d

$$d≔5\sqrt{2}$$