Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -5x=30
-
Equation 3*x^2=18*x
-
Equation 16*x^2-9=0
-
Equation 0*x=5
- Express {x} in terms of y where:
- 10*x-18*y=-6
- 3*x-12*y=-14
- 16*x+11*y=-14
- -4*x+20*y=-14
- Derivative of:
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3*x^2
- Integral of d{x}:
-
3*x^2
- Graphing y =:
- 3*x^2
- Limit of the function:
-
18*x
-
Identical expressions
- three *x^ two = eighteen *x
- 3 multiply by x squared equally 18 multiply by x
- three multiply by x to the power of two equally eighteen multiply by x
- 3*x2=18*x
- 3*x²=18*x
- 3*x to the power of 2=18*x
- 3x^2=18x
- 3x2=18x
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Similar expressions
- (x+2018)(x+2019)(x+2020)=(2019)(x+2020)(x+2021)
- (-10,5*10^(-3))+(5*((x^(2)))/(2*1216))+(14*((x-1)^(2))/(2*1216))-(18*((x-1)^(3))/(6*1216))=0
- x^3+18x+15=0
- 1/(16x+26)=1/(18x−24)
3*x^2=18*x 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
$$3 x^{2} = 18 x$$
to
$$3 x^{2} - 18 x = 0$$
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
$$a = 3$$
$$b = -18$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6$$
$$x_{2} = 0$$
left part with negative sign.
The equation is transformed from
$$3 x^{2} = 18 x$$
to
$$3 x^{2} - 18 x = 0$$
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
$$a = 3$$
$$b = -18$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(-18)^2 - 4 * (3) * (0) = 324
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6$$
$$x_{2} = 0$$
Vieta's Theorem
rewrite the equation
$$3 x^{2} = 18 x$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 6 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = 0$$
$$3 x^{2} = 18 x$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 6 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = 0$$
The graph