Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3*x^2-x-5=0
-
Equation cos(x)=-3
-
Equation x²-6x+5=0
-
Equation (5+7*a)*15=-30
- Express {x} in terms of y where:
- -2*x+15*y=9
- -15*x-19*y=-2
- -5*x+15*y=6
- -17*x+7*y=-11
- Sum of series:
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-6
- Limit of the function:
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-6
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Identical expressions
- (x- two)(x+ three)=- six
- (x minus 2)(x plus 3) equally minus 6
- (x minus two)(x plus three) equally minus six
- x-2x+3=-6
-
Similar expressions
- (5-x)-(2*x+3)=5
- 7x-(2x+3)=0
- (x+2)(x+3)=-6
- (x-2)(x-3)=-6
- (x+3)*(x+5)-(x-2)*(x+3)=0
- (5-x)-(2x+3)=5
- (x-2)(x+3)=+6
(x-2)(x+3)=-6 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
$$\left(x - 2\right) \left(x + 3\right) = -6$$
to
$$\left(x - 2\right) \left(x + 3\right) + 6 = 0$$
Expand the expression in the equation
$$\left(x - 2\right) \left(x + 3\right) + 6 = 0$$
We get the quadratic equation
$$x^{2} + x = 0$$
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
$$x_{1} = 0$$
$$x_{2} = -1$$
left part with negative sign.
The equation is transformed from
$$\left(x - 2\right) \left(x + 3\right) = -6$$
to
$$\left(x - 2\right) \left(x + 3\right) + 6 = 0$$
Expand the expression in the equation
$$\left(x - 2\right) \left(x + 3\right) + 6 = 0$$
We get the quadratic equation
$$x^{2} + x = 0$$
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
$$x_{1} = 0$$
$$x_{2} = -1$$
The graph