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Identical expressions
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Similar expressions
- 5,6(x-10)(x-33)=0
- 5,6(x+10)(x+33)=0
5,6(x-10)(x+33)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
28*(x - 10)
-----------*(x + 33) = 0
5
$$\frac{28 \left(x - 10\right)}{5} \left(x + 33\right) = 0$$
Detail solution
Expand the expression in the equation
$$\frac{28 \left(x - 10\right)}{5} \left(x + 33\right) = 0$$
We get the quadratic equation
$$\frac{28 x^{2}}{5} + \frac{644 x}{5} - 1848 = 0$$
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
$$a = \frac{28}{5}$$
$$b = \frac{644}{5}$$
$$c = -1848$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 10$$
$$x_{2} = -33$$
$$\frac{28 \left(x - 10\right)}{5} \left(x + 33\right) = 0$$
We get the quadratic equation
$$\frac{28 x^{2}}{5} + \frac{644 x}{5} - 1848 = 0$$
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
$$a = \frac{28}{5}$$
$$b = \frac{644}{5}$$
$$c = -1848$$
, then
D = b^2 - 4 * a * c =
(644/5)^2 - 4 * (28/5) * (-1848) = 1449616/25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 10$$
$$x_{2} = -33$$
Sum and product of roots
[src]
sum
-33 + 10
$$-33 + 10$$
=
-23
$$-23$$
product
-33*10
$$- 330$$
=
-330
$$-330$$
-330