Mister Exam
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How to use it?
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Equation x^2=-7
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Equation x^2-6*x+12=0
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Equation -2*x^3/(x^2-1)^2+2*x/(x^2-1)=0
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- Graphing y =:
- 2x²
- Derivative of:
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2x²
- Integral of d{x}:
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2x²
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Identical expressions
- (x+ two)²+(x-3²)=2x²
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Similar expressions
- (x-2)²+(x-3²)=2x²
- (x+2)²-(x-3²)=2x²
- (x+2)²+(x+3²)=2x²
(x+2)²+(x-3²)=2x² equation
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The solution
You have entered
[src]
2 2 (x + 2) + x - 9 = 2*x
$$\left(x - 9\right) + \left(x + 2\right)^{2} = 2 x^{2}$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(x - 9\right) + \left(x + 2\right)^{2} = 2 x^{2}$$
to
$$- 2 x^{2} + \left(\left(x - 9\right) + \left(x + 2\right)^{2}\right) = 0$$
Expand the expression in the equation
$$- 2 x^{2} + \left(\left(x - 9\right) + \left(x + 2\right)^{2}\right) = 0$$
We get the quadratic equation
$$- x^{2} + 5 x - 5 = 0$$
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
$$a = -1$$
$$b = 5$$
$$c = -5$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{5}{2} - \frac{\sqrt{5}}{2}$$
$$x_{2} = \frac{\sqrt{5}}{2} + \frac{5}{2}$$
left part with negative sign.
The equation is transformed from
$$\left(x - 9\right) + \left(x + 2\right)^{2} = 2 x^{2}$$
to
$$- 2 x^{2} + \left(\left(x - 9\right) + \left(x + 2\right)^{2}\right) = 0$$
Expand the expression in the equation
$$- 2 x^{2} + \left(\left(x - 9\right) + \left(x + 2\right)^{2}\right) = 0$$
We get the quadratic equation
$$- x^{2} + 5 x - 5 = 0$$
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
$$a = -1$$
$$b = 5$$
$$c = -5$$
, then
D = b^2 - 4 * a * c =
(5)^2 - 4 * (-1) * (-5) = 5
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{5}{2} - \frac{\sqrt{5}}{2}$$
$$x_{2} = \frac{\sqrt{5}}{2} + \frac{5}{2}$$
Rapid solution
[src]
___
5 \/ 5
x1 = - - -----
2 2
$$x_{1} = \frac{5}{2} - \frac{\sqrt{5}}{2}$$
___
5 \/ 5
x2 = - + -----
2 2
$$x_{2} = \frac{\sqrt{5}}{2} + \frac{5}{2}$$
x2 = sqrt(5)/2 + 5/2
Sum and product of roots
[src]
sum
___ ___ 5 \/ 5 5 \/ 5 - - ----- + - + ----- 2 2 2 2
$$\left(\frac{5}{2} - \frac{\sqrt{5}}{2}\right) + \left(\frac{\sqrt{5}}{2} + \frac{5}{2}\right)$$
=
5
$$5$$
product
/ ___\ / ___\ |5 \/ 5 | |5 \/ 5 | |- - -----|*|- + -----| \2 2 / \2 2 /
$$\left(\frac{5}{2} - \frac{\sqrt{5}}{2}\right) \left(\frac{\sqrt{5}}{2} + \frac{5}{2}\right)$$
=
5
$$5$$
5