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(2x-1)² equation

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Numerical solution:

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The solution

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         2    
(2*x - 1)  = 0
$$\left(2 x - 1\right)^{2} = 0$$
Detail solution
Expand the expression in the equation
$$\left(2 x - 1\right)^{2} = 0$$
We get the quadratic equation
$$4 x^{2} - 4 x + 1 = 0$$
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
$$a = 4$$
$$b = -4$$
$$c = 1$$
, then
D = b^2 - 4 * a * c = 

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

Because D = 0, then the equation has one root.
x = -b/2a = --4/2/(4)

$$x_{1} = \frac{1}{2}$$
The graph
Rapid solution [src]
x1 = 1/2
$$x_{1} = \frac{1}{2}$$
x1 = 1/2
Sum and product of roots [src]
sum
1/2
$$\frac{1}{2}$$
=
1/2
$$\frac{1}{2}$$
product
1/2
$$\frac{1}{2}$$
=
1/2
$$\frac{1}{2}$$
1/2
Numerical answer [src]
x1 = 0.5
x1 = 0.5