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Equation 3(x-2)(x+4)=2x^2+x
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2x^2+x
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Identical expressions
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Similar expressions
- -(2x+3)/2-3x-2(x+4)/3=-1/2
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- 6-3x-2(x+4.5)=x-27
- 3(x+2)(x+4)=2x^2+x
3(x-2)(x+4)=2x^2+x equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
2 3*(x - 2)*(x + 4) = 2*x + x
$$3 \left(x - 2\right) \left(x + 4\right) = 2 x^{2} + x$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$3 \left(x - 2\right) \left(x + 4\right) = 2 x^{2} + x$$
to
$$3 \left(x - 2\right) \left(x + 4\right) + \left(- 2 x^{2} - x\right) = 0$$
Expand the expression in the equation
$$3 \left(x - 2\right) \left(x + 4\right) + \left(- 2 x^{2} - x\right) = 0$$
We get the quadratic equation
$$x^{2} + 5 x - 24 = 0$$
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
$$a = 1$$
$$b = 5$$
$$c = -24$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3$$
$$x_{2} = -8$$
left part with negative sign.
The equation is transformed from
$$3 \left(x - 2\right) \left(x + 4\right) = 2 x^{2} + x$$
to
$$3 \left(x - 2\right) \left(x + 4\right) + \left(- 2 x^{2} - x\right) = 0$$
Expand the expression in the equation
$$3 \left(x - 2\right) \left(x + 4\right) + \left(- 2 x^{2} - x\right) = 0$$
We get the quadratic equation
$$x^{2} + 5 x - 24 = 0$$
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
$$a = 1$$
$$b = 5$$
$$c = -24$$
, then
D = b^2 - 4 * a * c =
(5)^2 - 4 * (1) * (-24) = 121
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3$$
$$x_{2} = -8$$
Sum and product of roots
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sum
-8 + 3
$$-8 + 3$$
=
-5
$$-5$$
product
-8*3
$$- 24$$
=
-24
$$-24$$
-24
The graph