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Similar expressions
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(x+5)(2x-4)+24=0 equation
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The solution
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[src]
(x + 5)*(2*x - 4) + 24 = 0
$$\left(x + 5\right) \left(2 x - 4\right) + 24 = 0$$
Detail solution
Expand the expression in the equation
$$\left(x + 5\right) \left(2 x - 4\right) + 24 = 0$$
We get the quadratic equation
$$2 x^{2} + 6 x + 4 = 0$$
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
$$a = 2$$
$$b = 6$$
$$c = 4$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -1$$
$$x_{2} = -2$$
$$\left(x + 5\right) \left(2 x - 4\right) + 24 = 0$$
We get the quadratic equation
$$2 x^{2} + 6 x + 4 = 0$$
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
$$a = 2$$
$$b = 6$$
$$c = 4$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (2) * (4) = 4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -1$$
$$x_{2} = -2$$
Sum and product of roots
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sum
-2 - 1
$$-2 - 1$$
=
-3
$$-3$$
product
-2*(-1)
$$- -2$$
=
2
$$2$$
2
The graph