Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 2x=18-x
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Equation 9*x^2=54*x
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Equation cos(x)=-2
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Equation 2*x^2+6*x+9=
- Express {x} in terms of y where:
- 14*x+16*y=-3
- -10*x-18*y=15
- 20*x+5*y=-3
- 4*x+18*y=-14
- Derivative of:
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9*x^2
- Graphing y =:
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9*x^2
- Integral of d{x}:
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9*x^2
- Limit of the function:
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54*x
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Identical expressions
- nine *x^ two = fifty-four *x
- 9 multiply by x squared equally 54 multiply by x
- nine multiply by x to the power of two equally fifty minus four multiply by x
- 9*x2=54*x
- 9*x²=54*x
- 9*x to the power of 2=54*x
- 9x^2=54x
- 9x2=54x
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Similar expressions
- 2x^3-9x^2+25*x-24=0
- 1/(3x+1)-2/(3x-1)-5x/(9x^2-1)=(3x^2)/(1-9x^2)
- 7*(2*x-5)-5*(4*x+3)=4*x
- 4,86x+19,4x+0,54x=2020
- 1.5(4x-1,6)=x+1,6
- 5,5(4x+1)=22x+15
9*x^2=54*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
$$9 x^{2} = 54 x$$
to
$$9 x^{2} - 54 x = 0$$
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
$$a = 9$$
$$b = -54$$
$$c = 0$$
, 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
$$9 x^{2} = 54 x$$
to
$$9 x^{2} - 54 x = 0$$
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
$$a = 9$$
$$b = -54$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(-54)^2 - 4 * (9) * (0) = 2916
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
$$9 x^{2} = 54 x$$
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
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = 0$$
$$9 x^{2} = 54 x$$
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