Mister Exam
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How to use it?
- Equation:
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Equation (-5x+3)*(-x+6)=0
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Equation (x^2-2*x-3)/(x-3)=0
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Equation (x+3)^2=(x-4)^2
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Equation x^2-6x-7=0
- Express {x} in terms of y where:
- -2*x+13*y=-6
- 3*x-1*y=5
- -6*x-9*y=-20
- -8*x-8*y=14
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Identical expressions
- 6x^ two -36x- sixteen , five = zero
- 6x squared minus 36x minus 16,5 equally 0
- 6x to the power of two minus 36x minus sixteen , five equally zero
- 6x2-36x-16,5=0
- 6x²-36x-16,5=0
- 6x to the power of 2-36x-16,5=0
- 6x^2-36x-16,5=O
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Similar expressions
- 6x^2-36x+16,5=0
- 6x^2+36x-16,5=0
6x^2-36x-16,5=0 equation
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The solution
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[src]
2 33
6*x - 36*x - -- = 0
2
$$\left(6 x^{2} - 36 x\right) - \frac{33}{2} = 0$$
Detail solution
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
$$a = 6$$
$$b = -36$$
$$c = - \frac{33}{2}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3 + \frac{\sqrt{47}}{2}$$
$$x_{2} = 3 - \frac{\sqrt{47}}{2}$$
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
$$a = 6$$
$$b = -36$$
$$c = - \frac{33}{2}$$
, then
D = b^2 - 4 * a * c =
(-36)^2 - 4 * (6) * (-33/2) = 1692
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3 + \frac{\sqrt{47}}{2}$$
$$x_{2} = 3 - \frac{\sqrt{47}}{2}$$
Vieta's Theorem
rewrite the equation
$$\left(6 x^{2} - 36 x\right) - \frac{33}{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 6 x - \frac{11}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = - \frac{11}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = - \frac{11}{4}$$
$$\left(6 x^{2} - 36 x\right) - \frac{33}{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 6 x - \frac{11}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = - \frac{11}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = - \frac{11}{4}$$
Rapid solution
[src]
____
\/ 47
x1 = 3 - ------
2
$$x_{1} = 3 - \frac{\sqrt{47}}{2}$$
____
\/ 47
x2 = 3 + ------
2
$$x_{2} = 3 + \frac{\sqrt{47}}{2}$$
x2 = 3 + sqrt(47)/2
Sum and product of roots
[src]
sum
____ ____
\/ 47 \/ 47
3 - ------ + 3 + ------
2 2
$$\left(3 - \frac{\sqrt{47}}{2}\right) + \left(3 + \frac{\sqrt{47}}{2}\right)$$
=
6
$$6$$
product
/ ____\ / ____\ | \/ 47 | | \/ 47 | |3 - ------|*|3 + ------| \ 2 / \ 2 /
$$\left(3 - \frac{\sqrt{47}}{2}\right) \left(3 + \frac{\sqrt{47}}{2}\right)$$
=
-11/4
$$- \frac{11}{4}$$
-11/4