Solve T-sqrt{4x+5}=-1

$$T - \sqrt { 4 x + 5 } = - 1$$

Solve for x

$$x=\frac{\left(T+1\right)^{2}-5}{4}$$

$$T+1\geq 0$$

Steps for Solving Radical Equations

Subtract T from both sides of the equation.

$$-\sqrt{4x+5}+T-T=-1-T$$

Subtracting T from itself leaves 0.

$$-\sqrt{4x+5}=-1-T$$

Subtract T from -1.

$$-\sqrt{4x+5}=-T-1$$

Divide both sides by -1.

$$\frac{-\sqrt{4x+5}}{-1}=\frac{-T-1}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{4x+5}=\frac{-T-1}{-1}$$

Divide -1-T by -1.

$$\sqrt{4x+5}=T+1$$

Square both sides of the equation.

$$4x+5=\left(T+1\right)^{2}$$

Subtract 5 from both sides of the equation.

$$4x+5-5=\left(T+1\right)^{2}-5$$

Subtracting 5 from itself leaves 0.

$$4x=\left(T+1\right)^{2}-5$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{\left(T+1\right)^{2}-5}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{\left(T+1\right)^{2}-5}{4}$$

Solve for T (complex solution)

$$T=\sqrt{4x+5}-1$$

Solve for x (complex solution)

$$x=\frac{\left(T+1\right)^{2}-5}{4}$$

$$T=-1\text{ or }arg(T+1)<\pi$$

Solve for T

$$T=\sqrt{4x+5}-1$$

$$x\geq -\frac{5}{4}$$