Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 2*x^2-x+5=0
-
Equation e^x=1
-
Equation x^2+2=x+2
-
Equation 5=12-5(4x-1)
- Express {x} in terms of y where:
- -12*x-2*y=-15
- -4*x+4*y=-9
- -19*x-2*y=-6
- -2*x+2*y=4
- Derivative of:
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x^2+2
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x+2
- Inequation:
- x^2+2
- x+2
- Integral of d{x}:
-
x^2+2
-
x+2
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Identical expressions
- x^ two + two =x+ two
- x squared plus 2 equally x plus 2
- x to the power of two plus two equally x plus two
- x2+2=x+2
- x²+2=x+2
- x to the power of 2+2=x+2
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Similar expressions
- x^2-2=x+2
- 4x-3x^2+2=0
- x^2+2=x-2
x^2+2=x+2 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
$$x^{2} + 2 = x + 2$$
to
$$\left(- x - 2\right) + \left(x^{2} + 2\right) = 0$$
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
$$a = 1$$
$$b = -1$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1$$
$$x_{2} = 0$$
left part with negative sign.
The equation is transformed from
$$x^{2} + 2 = x + 2$$
to
$$\left(- x - 2\right) + \left(x^{2} + 2\right) = 0$$
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
$$a = 1$$
$$b = -1$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (0) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1$$
$$x_{2} = 0$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = 0$$
The graph