Mister Exam

(x-3)(x+4)=x(1-x) equation

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Numerical solution:

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The solution

You have entered [src]
(x - 3)*(x + 4) = x*(1 - x)
$$\left(x - 3\right) \left(x + 4\right) = x \left(1 - x\right)$$
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
$$\left(x - 3\right) \left(x + 4\right) = x \left(1 - x\right)$$
to
$$- x \left(1 - x\right) + \left(x - 3\right) \left(x + 4\right) = 0$$
Expand the expression in the equation
$$- x \left(1 - x\right) + \left(x - 3\right) \left(x + 4\right) = 0$$
We get the quadratic equation
$$2 x^{2} - 12 = 0$$
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
$$a = 2$$
$$b = 0$$
$$c = -12$$
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (2) * (-12) = 96

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = \sqrt{6}$$
$$x_{2} = - \sqrt{6}$$
The graph
Sum and product of roots [src]
sum
    ___     ___
- \/ 6  + \/ 6 
$$- \sqrt{6} + \sqrt{6}$$
=
0
$$0$$
product
   ___   ___
-\/ 6 *\/ 6 
$$- \sqrt{6} \sqrt{6}$$
=
-6
$$-6$$
-6
Rapid solution [src]
        ___
x1 = -\/ 6 
$$x_{1} = - \sqrt{6}$$
       ___
x2 = \/ 6 
$$x_{2} = \sqrt{6}$$
x2 = sqrt(6)
Numerical answer [src]
x1 = 2.44948974278318
x2 = -2.44948974278318
x2 = -2.44948974278318
The graph
(x-3)(x+4)=x(1-x) equation