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(x+6)(2x+6)-20=0 equation
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The solution
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[src]
(x + 6)*(2*x + 6) - 20 = 0
$$\left(x + 6\right) \left(2 x + 6\right) - 20 = 0$$
Detail solution
Expand the expression in the equation
$$\left(x + 6\right) \left(2 x + 6\right) - 20 = 0$$
We get the quadratic equation
$$2 x^{2} + 18 x + 16 = 0$$
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
$$a = 2$$
$$b = 18$$
$$c = 16$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -1$$
$$x_{2} = -8$$
$$\left(x + 6\right) \left(2 x + 6\right) - 20 = 0$$
We get the quadratic equation
$$2 x^{2} + 18 x + 16 = 0$$
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
$$a = 2$$
$$b = 18$$
$$c = 16$$
, then
D = b^2 - 4 * a * c =
(18)^2 - 4 * (2) * (16) = 196
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -1$$
$$x_{2} = -8$$
Sum and product of roots
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sum
-8 - 1
$$-8 - 1$$
=
-9
$$-9$$
product
-8*(-1)
$$- -8$$
=
8
$$8$$
8
The graph