Mister Exam
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How to use it?
- Equation:
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Equation 3*x^2-x-5=0
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Equation 4^x-6*2^x+8=0
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Equation x+20=20+x
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- 5(x-2)
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Identical expressions
- five (x- two)=(3x+ two)(x- two)
- 5(x minus 2) equally (3x plus 2)(x minus 2)
- five (x minus two) equally (3x plus two)(x minus two)
- 5x-2=3x+2x-2
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Similar expressions
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- 5(x-2)=(3x-2)(x-2)
- 3^(x)+2*x-2=0
- 258*5^x-25*2^x=100
- 5(x+2)=(3x+2)(x-2)
- 3*(x+2)*(x-2)*(x^2+4)=0
- 5(x-2,2)=7x
5(x-2)=(3x+2)(x-2) equation
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The solution
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5*(x - 2) = (3*x + 2)*(x - 2)
$$5 \left(x - 2\right) = \left(x - 2\right) \left(3 x + 2\right)$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$5 \left(x - 2\right) = \left(x - 2\right) \left(3 x + 2\right)$$
to
$$- \left(x - 2\right) \left(3 x + 2\right) + 5 \left(x - 2\right) = 0$$
Expand the expression in the equation
$$- \left(x - 2\right) \left(3 x + 2\right) + 5 \left(x - 2\right) = 0$$
We get the quadratic equation
$$- 3 x^{2} + 9 x - 6 = 0$$
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
$$a = -3$$
$$b = 9$$
$$c = -6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1$$
$$x_{2} = 2$$
left part with negative sign.
The equation is transformed from
$$5 \left(x - 2\right) = \left(x - 2\right) \left(3 x + 2\right)$$
to
$$- \left(x - 2\right) \left(3 x + 2\right) + 5 \left(x - 2\right) = 0$$
Expand the expression in the equation
$$- \left(x - 2\right) \left(3 x + 2\right) + 5 \left(x - 2\right) = 0$$
We get the quadratic equation
$$- 3 x^{2} + 9 x - 6 = 0$$
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
$$a = -3$$
$$b = 9$$
$$c = -6$$
, then
D = b^2 - 4 * a * c =
(9)^2 - 4 * (-3) * (-6) = 9
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1$$
$$x_{2} = 2$$