Solve 5(x+5)+4=x+2sqrt{m}

$$5 ( x + 5 ) + 4 = x + 2 \sqrt { m }$$

Solve for x (complex solution)

$$x=\frac{\sqrt{m}}{2}-\frac{29}{4}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x+5.

$$5x+25+4=x+2\sqrt{m}$$

Add 25 and 4 to get 29.

$$5x+29=x+2\sqrt{m}$$

Subtract x from both sides.

$$5x+29-x=2\sqrt{m}$$

Combine 5x and -x to get 4x.

$$4x+29=2\sqrt{m}$$

Subtract 29 from both sides.

$$4x=2\sqrt{m}-29$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{2\sqrt{m}-29}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{2\sqrt{m}-29}{4}$$

Divide 2\sqrt{m}-29 by 4.

$$x=\frac{\sqrt{m}}{2}-\frac{29}{4}$$

Solve for m

$$m=\frac{\left(4x+29\right)^{2}}{4}$$

$$2x+\frac{29}{2}\geq 0$$

Steps for Solving Radical Equations

Use the distributive property to multiply 5 by x+5.

$$5x+25+4=x+2\sqrt{m}$$

Add 25 and 4 to get 29.

$$5x+29=x+2\sqrt{m}$$

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

$$x+2\sqrt{m}=5x+29$$

Subtract x from both sides.

$$2\sqrt{m}=5x+29-x$$

Combine 5x and -x to get 4x.

$$2\sqrt{m}=4x+29$$

Divide both sides by 2.

$$\frac{2\sqrt{m}}{2}=\frac{4x+29}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\sqrt{m}=\frac{4x+29}{2}$$

Divide 4x+29 by 2.

$$\sqrt{m}=2x+\frac{29}{2}$$

Square both sides of the equation.

$$m=\frac{\left(4x+29\right)^{2}}{4}$$

Solve for x

$$x=\frac{\sqrt{m}}{2}-\frac{29}{4}$$

$$m\geq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x+5.

$$5x+25+4=x+2\sqrt{m}$$

Add 25 and 4 to get 29.

$$5x+29=x+2\sqrt{m}$$

Subtract x from both sides.

$$5x+29-x=2\sqrt{m}$$

Combine 5x and -x to get 4x.

$$4x+29=2\sqrt{m}$$

Subtract 29 from both sides.

$$4x=2\sqrt{m}-29$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{2\sqrt{m}-29}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{2\sqrt{m}-29}{4}$$

Divide 2\sqrt{m}-29 by 4.

$$x=\frac{\sqrt{m}}{2}-\frac{29}{4}$$

Solve for m (complex solution)

$$m=\frac{\left(4x+29\right)^{2}}{4}$$

$$x=-\frac{29}{4}\text{ or }arg(2x+\frac{29}{2})<\pi$$