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- Equation:
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Equation (-5x+3)*(-x+6)=0
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Equation (x^2-2*x-3)/(x-3)=0
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Equation (x+3)^2=(x-4)^2
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Equation 4(5-n)-3(2n+7)=0
- Express {x} in terms of y where:
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Identical expressions
- (-5x+ three)(-x+ six)
- ( minus 5x plus 3)( minus x plus 6)
- ( minus 5x plus three)( minus x plus six)
- -5x+3-x+6
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Similar expressions
- (-5x+3)*(-x+6)=0
- (-5x+3)(x+6)
- (-5x-3)(-x+6)
- (5x+3)(-x+6)
- (-5x+3)(-x-6)
- (-5*x+3)*(-x+6)=0
(-5x+3)(-x+6) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(3 - 5 x\right) \left(6 - x\right) = 0$$
We get the quadratic equation
$$5 x^{2} - 33 x + 18 = 0$$
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
$$a = 5$$
$$b = -33$$
$$c = 18$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6$$
$$x_{2} = \frac{3}{5}$$
$$\left(3 - 5 x\right) \left(6 - x\right) = 0$$
We get the quadratic equation
$$5 x^{2} - 33 x + 18 = 0$$
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
$$a = 5$$
$$b = -33$$
$$c = 18$$
, then
D = b^2 - 4 * a * c =
(-33)^2 - 4 * (5) * (18) = 729
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6$$
$$x_{2} = \frac{3}{5}$$
Sum and product of roots
[src]
sum
6 + 3/5
$$\frac{3}{5} + 6$$
=
33/5
$$\frac{33}{5}$$
product
6*3 --- 5
$$\frac{3 \cdot 6}{5}$$
=
18/5
$$\frac{18}{5}$$
18/5