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(x-6)^2=-24x

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

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Numerical solution:

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The solution

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

The equation is transformed from
(x−6)2=−24x\left(x - 6\right)^{2} = - 24 x
to
24x+(x−6)2=024 x + \left(x - 6\right)^{2} = 0
Expand the expression in the equation
24x+(x−6)2=024 x + \left(x - 6\right)^{2} = 0
We get the quadratic equation
x2+12x+36=0x^{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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=12b = 12
c=36c = 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)

x1=−6x_{1} = -6
The graph
402-16-14-12-10-8-6-4-2-500500
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-6
−6-6 
=
-6
−6-6 
product
-6
−6-6 
=
-6
−6-6 
-6
Rapid solution [src] 
x1 = -6
x1=−6x_{1} = -6 
x1 = -6
Numerical answer [src] 
x1 = -6.0
x1 = -6.0
The graph
(x-6)^2=-24x equation
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