Mister Exam
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How to use it?
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x^2+2x
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Identical expressions
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Similar expressions
- 2x+4x+2=0
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- x^2+2x-3
- 2(x+4)(x+2)=x^2-2x
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2(x+4)(x+2)=x^2+2x equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 2*(x + 4)*(x + 2) = x + 2*x
$$\left(x + 2\right) 2 \left(x + 4\right) = x^{2} + 2 x$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(x + 2\right) 2 \left(x + 4\right) = x^{2} + 2 x$$
to
$$\left(x + 2\right) 2 \left(x + 4\right) + \left(- x^{2} - 2 x\right) = 0$$
Expand the expression in the equation
$$\left(x + 2\right) 2 \left(x + 4\right) + \left(- x^{2} - 2 x\right) = 0$$
We get the quadratic equation
$$x^{2} + 10 x + 16 = 0$$
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
$$a = 1$$
$$b = 10$$
$$c = 16$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -2$$
$$x_{2} = -8$$
left part with negative sign.
The equation is transformed from
$$\left(x + 2\right) 2 \left(x + 4\right) = x^{2} + 2 x$$
to
$$\left(x + 2\right) 2 \left(x + 4\right) + \left(- x^{2} - 2 x\right) = 0$$
Expand the expression in the equation
$$\left(x + 2\right) 2 \left(x + 4\right) + \left(- x^{2} - 2 x\right) = 0$$
We get the quadratic equation
$$x^{2} + 10 x + 16 = 0$$
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
$$a = 1$$
$$b = 10$$
$$c = 16$$
, then
D = b^2 - 4 * a * c =
(10)^2 - 4 * (1) * (16) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -2$$
$$x_{2} = -8$$
Sum and product of roots
[src]
sum
-8 - 2
$$-8 - 2$$
=
-10
$$-10$$
product
-8*(-2)
$$- -16$$
=
16
$$16$$
16
The graph