Solve b*4sqrt{x}=5-10sqrt{x}

$$b \cdot 4 \sqrt { x } = 5 - 10 \sqrt { x }$$

Solve for b

$$b=-\frac{5}{2}+\frac{5}{4\sqrt{x}}$$

$$x>0$$

Steps for Solving Linear Equation

Multiply -1 and 10 to get -10.

$$4b\sqrt{x}=5-10\sqrt{x}$$

The equation is in standard form.

$$4\sqrt{x}b=-10\sqrt{x}+5$$

Divide both sides by 4\sqrt{x}.

$$\frac{4\sqrt{x}b}{4\sqrt{x}}=\frac{-10\sqrt{x}+5}{4\sqrt{x}}$$

Dividing by 4\sqrt{x} undoes the multiplication by 4\sqrt{x}.

$$b=\frac{-10\sqrt{x}+5}{4\sqrt{x}}$$

Divide 5-10\sqrt{x} by 4\sqrt{x}.

$$b=-\frac{5}{2}+\frac{5}{4\sqrt{x}}$$

Solve for x

$$x=\frac{25}{4\left(2b+5\right)^{2}}$$

$$b>-\frac{5}{2}$$

Steps for Solving Radical Equations

Add 10\sqrt{x} to both sides.

$$4b\sqrt{x}+10\sqrt{x}=5$$

Combine all terms containing x.

$$\left(4b+10\right)\sqrt{x}=5$$

Divide both sides by 4b+10.

$$\frac{\left(4b+10\right)\sqrt{x}}{4b+10}=\frac{5}{4b+10}$$

Dividing by 4b+10 undoes the multiplication by 4b+10.

$$\sqrt{x}=\frac{5}{4b+10}$$

Divide 5 by 4b+10.

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

Square both sides of the equation.

$$x=\frac{25}{4\left(2b+5\right)^{2}}$$