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(x-6)^2=-24*x

(x-6)^2=-24*x equation

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Numerical solution:

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The solution

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(x - 6)  = -24*x
$$\left(x - 6\right)^{2} = - 24 x$$
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
$$\left(x - 6\right)^{2} = - 24 x$$
to
$$24 x + \left(x - 6\right)^{2} = 0$$
Expand the expression in the equation
$$24 x + \left(x - 6\right)^{2} = 0$$
We get the quadratic equation
$$x^{2} + 12 x + 36 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 12$$
$$c = 36$$
, then
D = b^2 - 4 * a * c = 

(12)^2 - 4 * (1) * (36) = 0

Because D = 0, then the equation has one root.
x = -b/2a = -12/2/(1)

$$x_{1} = -6$$
The graph
Rapid solution [src]
x1 = -6
$$x_{1} = -6$$
x1 = -6
Sum and product of roots [src]
sum
-6
$$-6$$
=
-6
$$-6$$
product
-6
$$-6$$
=
-6
$$-6$$
-6
Numerical answer [src]
x1 = -6.0
x1 = -6.0
The graph
(x-6)^2=-24*x equation