Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 9-8*x=-9*x+15
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Equation x+14=8
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Equation 6*x=12
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Equation 2*6-y+2=0
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- -16*x-9*y=-1
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Identical expressions
- (6x- three)(-x+ three)= zero
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Similar expressions
- (6x-3)(-x-3)=0
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(6x-3)(-x+3)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(3 - x\right) \left(6 x - 3\right) = 0$$
We get the quadratic equation
$$- 6 x^{2} + 21 x - 9 = 0$$
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
$$a = -6$$
$$b = 21$$
$$c = -9$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{1}{2}$$
$$x_{2} = 3$$
$$\left(3 - x\right) \left(6 x - 3\right) = 0$$
We get the quadratic equation
$$- 6 x^{2} + 21 x - 9 = 0$$
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
$$a = -6$$
$$b = 21$$
$$c = -9$$
, then
D = b^2 - 4 * a * c =
(21)^2 - 4 * (-6) * (-9) = 225
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{2}$$
$$x_{2} = 3$$
Sum and product of roots
[src]
sum
1/2 + 3
$$\frac{1}{2} + 3$$
=
7/2
$$\frac{7}{2}$$
product
3 - 2
$$\frac{3}{2}$$
=
3/2
$$\frac{3}{2}$$
3/2
The graph