Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+7)*(x-1)=0
-
Equation x/3+x/4=-21
-
Equation sin(x)=0
-
Equation x^3-9*x=0
- Express {x} in terms of y where:
- 1*x+20*y=6
- -2*x+4*y=3
- 5*x+13*y=-15
- 3*x-17*y=-6
- Sum of series:
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-1
- Derivative of:
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-1
- Integral of d{x}:
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-1
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Identical expressions
- - one -(x- two)^ two =- one
- minus 1 minus (x minus 2) squared equally minus 1
- minus one minus (x minus two) to the power of two equally minus one
- -1-(x-2)2=-1
- -1-x-22=-1
- -1-(x-2)²=-1
- -1-(x-2) to the power of 2=-1
- -1-x-2^2=-1
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Similar expressions
- -1-(x-2)^2=+1
- -1+(x-2)^2=-1
- -1-(x+2)^2=-1
- 1-(x-2)^2=-1
-1-(x-2)^2=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$- \left(x - 2\right)^{2} - 1 = -1$$
to
$$\left(- \left(x - 2\right)^{2} - 1\right) + 1 = 0$$
Expand the expression in the equation
$$\left(- \left(x - 2\right)^{2} - 1\right) + 1 = 0$$
We get the quadratic equation
$$- x^{2} + 4 x - 4 = 0$$
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
$$a = -1$$
$$b = 4$$
$$c = -4$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = 2$$
left part with negative sign.
The equation is transformed from
$$- \left(x - 2\right)^{2} - 1 = -1$$
to
$$\left(- \left(x - 2\right)^{2} - 1\right) + 1 = 0$$
Expand the expression in the equation
$$\left(- \left(x - 2\right)^{2} - 1\right) + 1 = 0$$
We get the quadratic equation
$$- x^{2} + 4 x - 4 = 0$$
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
$$a = -1$$
$$b = 4$$
$$c = -4$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (-1) * (-4) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -4/2/(-1)
$$x_{1} = 2$$