Find x if `x(x-4x)=-4`

Answer

To solve the equation \( x(x - 4x) = -4 \), we can follow these steps:

### Step 1: Simplify the expression inside the parentheses
The expression \( x - 4x \) can be simplified:
\[ x - 4x = -3x \]
So the equation becomes:
\[ x(-3x) = -4 \]

### Step 2: Rewrite the equation
Now, we can rewrite the equation as:
\[ -3x^2 = -4 \]

### Step 3: Eliminate the negative sign
To eliminate the negative sign, we can multiply both sides of the equation by -1:
\[ 3x^2 = 4 \]

### Step 4: Divide both sides by 3
Next, we divide both sides by 3 to isolate \( x^2 \):
\[ x^2 = \frac{4}{3} \]

### Step 5: Take the square root of both sides
Now, we take the square root of both sides to solve for \( x \):
\[ x = \pm \sqrt{\frac{4}{3}} \]

### Step 6: Simplify the square root
The square root can be simplified:
\[ x = \pm \frac{\sqrt{4}}{\sqrt{3}} = \pm \frac{2}{\sqrt{3}} \]

### Final Answer
Thus, the solutions for \( x \) are:
\[ x = \frac{2}{\sqrt{3}} \quad \text{or} \quad x = -\frac{2}{\sqrt{3}} \]

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