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-7,2(x-13)(x+2,9)=0 equation
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The solution
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[src]
-36*(x - 13) / 29\
------------*|x + --| = 0
5 \ 10/
$$- \frac{36 \left(x - 13\right)}{5} \left(x + \frac{29}{10}\right) = 0$$
Detail solution
Expand the expression in the equation
$$- \frac{36 \left(x - 13\right)}{5} \left(x + \frac{29}{10}\right) = 0$$
We get the quadratic equation
$$- \frac{36 x^{2}}{5} + \frac{1818 x}{25} + \frac{6786}{25} = 0$$
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
$$a = - \frac{36}{5}$$
$$b = \frac{1818}{25}$$
$$c = \frac{6786}{25}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{29}{10}$$
$$x_{2} = 13$$
$$- \frac{36 \left(x - 13\right)}{5} \left(x + \frac{29}{10}\right) = 0$$
We get the quadratic equation
$$- \frac{36 x^{2}}{5} + \frac{1818 x}{25} + \frac{6786}{25} = 0$$
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
$$a = - \frac{36}{5}$$
$$b = \frac{1818}{25}$$
$$c = \frac{6786}{25}$$
, then
D = b^2 - 4 * a * c =
(1818/25)^2 - 4 * (-36/5) * (6786/25) = 8191044/625
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{29}{10}$$
$$x_{2} = 13$$
Sum and product of roots
[src]
sum
29
13 - --
10
$$- \frac{29}{10} + 13$$
=
101 --- 10
$$\frac{101}{10}$$
product
13*(-29) -------- 10
$$\frac{\left(-29\right) 13}{10}$$
=
-377 ----- 10
$$- \frac{377}{10}$$
-377/10