1. Expand (x + 6)² :
(x + 6)² = x² + 12x + 36
2. Set up the equation:
x² + 12x + 36 = 12x
3. Subtract ( 12x ) from both sides:
x² + 12x + 36 - 12x = 12x - 12x
4. Simplify the equation:
x² + 36 = 0
So now we have a simplified quadratic equation:
x² + 36 = 0
To solve for ( x ), we isolate ( x²):
x² = -36
Since we have a negative number on the right side, the solutions will involve imaginary numbers. Taking the square root of both sides gives:
[tex]x = \pm \sqrt{-36}[/tex]
We know that \(
[tex]\sqrt{-36} = \sqrt{36} \cdot \sqrt{-1} \), and \: \( \sqrt{-1} \)[/tex]
is represented by the imaginary unit ( i ). Thus:
[tex]x = \pm 6i[/tex]
The solutions to the quadratic equation ( + 6)² = 12x ) are:
[tex] x = 6i \quad \text{and} \quad x = -6i[/tex]
These are the imaginary solutions to the given quadratic equation.
