Solve frac{sqrt{5}}{2}+frac{sqrt{55}}{3+2}=x+7

$$\frac { \sqrt { 5 } } { 2 } + \frac { \sqrt { 55 } } { 3 + 2 } = x + 7$$

Solve for x

$$x=\frac{\sqrt{5}}{2}+\frac{\sqrt{55}}{5}-7\approx -4.398726314$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$\sqrt{5}+\frac{2}{5}\sqrt{55}=2x+14$$

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

$$2x+14=\sqrt{5}+\frac{2}{5}\sqrt{55}$$

Subtract 14 from both sides.

$$2x=\sqrt{5}+\frac{2}{5}\sqrt{55}-14$$

The equation is in standard form.

$$2x=\frac{2\sqrt{55}}{5}+\sqrt{5}-14$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{\frac{2\sqrt{55}}{5}+\sqrt{5}-14}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{\frac{2\sqrt{55}}{5}+\sqrt{5}-14}{2}$$

Divide \sqrt{5}+\frac{2\sqrt{55}}{5}-14 by 2.

$$x=\frac{\sqrt{5}}{2}+\frac{\sqrt{55}}{5}-7$$