Solve (sqrt{5}+sqrt{2})b=-10-2sqrt{10}

$$( \sqrt { 5 } + \sqrt { 2 } ) b = - 10 - 2 \sqrt { 10 }$$

Solve for b

$$b=-2\sqrt{5}\approx -4.472135955$$

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{5}+\sqrt{2} by b.

$$\sqrt{5}b+\sqrt{2}b=-10-2\sqrt{10}$$

Combine all terms containing b.

$$\left(\sqrt{5}+\sqrt{2}\right)b=-10-2\sqrt{10}$$

The equation is in standard form.

$$\left(\sqrt{2}+\sqrt{5}\right)b=-2\sqrt{10}-10$$

Divide both sides by \sqrt{5}+\sqrt{2}.

$$\frac{\left(\sqrt{2}+\sqrt{5}\right)b}{\sqrt{2}+\sqrt{5}}=\frac{-2\sqrt{10}-10}{\sqrt{2}+\sqrt{5}}$$

Dividing by \sqrt{5}+\sqrt{2} undoes the multiplication by \sqrt{5}+\sqrt{2}.

$$b=\frac{-2\sqrt{10}-10}{\sqrt{2}+\sqrt{5}}$$

Divide -10-2\sqrt{10} by \sqrt{5}+\sqrt{2}.

$$b=-2\sqrt{5}$$