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Identical expressions
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Similar expressions
- 4+4*(x-3)*(3*x-11)=0
- 4-4*(x+3)*(3*x-11)=0
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4-4*(x-3)*(3*x-11)=0 equation
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The solution
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[src]
4 - 4*(x - 3)*(3*x - 11) = 0
$$- 4 \left(x - 3\right) \left(3 x - 11\right) + 4 = 0$$
Detail solution
Expand the expression in the equation
$$- 4 \left(x - 3\right) \left(3 x - 11\right) + 4 = 0$$
We get the quadratic equation
$$- 12 x^{2} + 80 x - 128 = 0$$
This equation is of the form
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
$$a = -12$$
$$b = 80$$
$$c = -128$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{8}{3}$$
$$x_{2} = 4$$
$$- 4 \left(x - 3\right) \left(3 x - 11\right) + 4 = 0$$
We get the quadratic equation
$$- 12 x^{2} + 80 x - 128 = 0$$
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
$$a = -12$$
$$b = 80$$
$$c = -128$$
, then
D = b^2 - 4 * a * c =
(80)^2 - 4 * (-12) * (-128) = 256
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{8}{3}$$
$$x_{2} = 4$$
Sum and product of roots
[src]
sum
4 + 8/3
$$\frac{8}{3} + 4$$
=
20/3
$$\frac{20}{3}$$
product
4*8 --- 3
$$\frac{4 \cdot 8}{3}$$
=
32/3
$$\frac{32}{3}$$
32/3