Solve x=28/4+sqrt{2}

$$x = \frac { 28 } { 4 + \sqrt { 2 } }$$

Solve for x

$$x=8-2\sqrt{2}\approx 5.171572875$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{28}{4+\sqrt{2}} by multiplying numerator and denominator by 4-\sqrt{2}.

$$x=\frac{28\left(4-\sqrt{2}\right)}{\left(4+\sqrt{2}\right)\left(4-\sqrt{2}\right)}$$

Consider \left(4+\sqrt{2}\right)\left(4-\sqrt{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x=\frac{28\left(4-\sqrt{2}\right)}{4^{2}-\left(\sqrt{2}\right)^{2}}$$

Square 4. Square \sqrt{2}.

$$x=\frac{28\left(4-\sqrt{2}\right)}{16-2}$$

Subtract 2 from 16 to get 14.

$$x=\frac{28\left(4-\sqrt{2}\right)}{14}$$

Divide 28\left(4-\sqrt{2}\right) by 14 to get 2\left(4-\sqrt{2}\right).

$$x=2\left(4-\sqrt{2}\right)$$

Use the distributive property to multiply 2 by 4-\sqrt{2}.

$$x=8-2\sqrt{2}$$

Assign x

$$x≔8-2\sqrt{2}$$