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Quadratic equation what are the formula of this (×+6)²=12×​

Sagot :

Carmelafranchescabuyidn

Answer:

The quadratic formula is given by the equation        , where    .

In this case, the quadratic equation you've provided is      . Let's expand and simplify this equation.

View image Carmelafranchescabuy
Jafif67556idn

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.

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