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Identical expressions
- − nine , two (x− nine)(x+ thirty)= zero
- −9,2(x−9)(x plus 30) equally 0
- − nine , two (x− nine)(x plus thirty) equally zero
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Similar expressions
- −9,2(x−9)(x-30)=0
−9,2(x−9)(x+30)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
-46*(x - 9)
-----------*(x + 30) = 0
5
$$- \frac{46 \left(x - 9\right)}{5} \left(x + 30\right) = 0$$
Detail solution
Expand the expression in the equation
$$- \frac{46 \left(x - 9\right)}{5} \left(x + 30\right) = 0$$
We get the quadratic equation
$$- \frac{46 x^{2}}{5} - \frac{966 x}{5} + 2484 = 0$$
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
$$a = - \frac{46}{5}$$
$$b = - \frac{966}{5}$$
$$c = 2484$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -30$$
$$x_{2} = 9$$
$$- \frac{46 \left(x - 9\right)}{5} \left(x + 30\right) = 0$$
We get the quadratic equation
$$- \frac{46 x^{2}}{5} - \frac{966 x}{5} + 2484 = 0$$
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
$$a = - \frac{46}{5}$$
$$b = - \frac{966}{5}$$
$$c = 2484$$
, then
D = b^2 - 4 * a * c =
(-966/5)^2 - 4 * (-46/5) * (2484) = 3218436/25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -30$$
$$x_{2} = 9$$
Sum and product of roots
[src]
sum
-30 + 9
$$-30 + 9$$
=
-21
$$-21$$
product
-30*9
$$- 270$$
=
-270
$$-270$$
-270