Solve 4x+(1-a)sqrt{x}-9=0

$$4 x + ( 1 - a ) \sqrt { x } - 9 = 0$$

Solve for a (complex solution)

$$a=x^{-\frac{1}{2}}\left(4x+\sqrt{x}-9\right)$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-a by \sqrt{x}.

$$4x+\sqrt{x}-a\sqrt{x}-9=0$$

Subtract 4x from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{x}-a\sqrt{x}-9=-4x$$

Subtract \sqrt{x} from both sides.

$$-a\sqrt{x}-9=-4x-\sqrt{x}$$

Add 9 to both sides.

$$-a\sqrt{x}=-4x-\sqrt{x}+9$$

The equation is in standard form.

$$\left(-\sqrt{x}\right)a=-4x-\sqrt{x}+9$$

Divide both sides by -\sqrt{x}.

$$\frac{\left(-\sqrt{x}\right)a}{-\sqrt{x}}=\frac{-4x-\sqrt{x}+9}{-\sqrt{x}}$$

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

$$a=\frac{-4x-\sqrt{x}+9}{-\sqrt{x}}$$

Divide -4x-\sqrt{x}+9 by -\sqrt{x}.

$$a=4\sqrt{x}+1-9x^{-\frac{1}{2}}$$

Solve for a

$$a=\frac{4x+\sqrt{x}-9}{\sqrt{x}}$$

$$x>0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-a by \sqrt{x}.

$$4x+\sqrt{x}-a\sqrt{x}-9=0$$

Subtract 4x from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{x}-a\sqrt{x}-9=-4x$$

Subtract \sqrt{x} from both sides.

$$-a\sqrt{x}-9=-4x-\sqrt{x}$$

Add 9 to both sides.

$$-a\sqrt{x}=-4x-\sqrt{x}+9$$

The equation is in standard form.

$$\left(-\sqrt{x}\right)a=-4x-\sqrt{x}+9$$

Divide both sides by -\sqrt{x}.

$$\frac{\left(-\sqrt{x}\right)a}{-\sqrt{x}}=\frac{-4x-\sqrt{x}+9}{-\sqrt{x}}$$

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

$$a=\frac{-4x-\sqrt{x}+9}{-\sqrt{x}}$$

Divide -4x-\sqrt{x}+9 by -\sqrt{x}.

$$a=4\sqrt{x}+1-\frac{9}{\sqrt{x}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\left(\sqrt{a^{2}-2a+145}-a+1\right)^{2}}{64}\text{, }&arg(\frac{\sqrt{a^{2}-2a+145}-a+1}{8})\geq \pi \\x=\frac{\left(-\sqrt{a^{2}-2a+145}-a+1\right)^{2}}{64}\text{, }&arg(\frac{-\sqrt{a^{2}-2a+145}-a+1}{8})\geq \pi \end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\left(-\sqrt{a^{2}-2a+145}-a+1\right)^{2}}{64}\text{, }&-\frac{-\sqrt{a^{2}-2a+145}-a+1}{8}\geq 0\end{matrix}\right.$$