Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 1/x^2-1/x-6=0
-
Equation x^2-8=0
-
Equation x^2=-3
-
Equation x^4-2*x^3+x^2-1=0
- Express {x} in terms of y where:
- -9*x-12*y=-19
- 6*x+7*y=-10
- 4*x-11*y=-2
- -5*x-2*y=-14
- Graphing y =:
- x^2-35
- 2x
- Integral of d{x}:
-
2x
- Derivative of:
-
2x
-
Identical expressions
- x^ two - thirty-five =2x
- x squared minus 35 equally 2x
- x to the power of two minus thirty minus five equally 2x
- x2-35=2x
- x²-35=2x
- x to the power of 2-35=2x
-
Similar expressions
- x^4-2*x^3+x^2-1=0
- x^2+35=2x
- x^3+2*x^2-9*x-18=0
x^2-35=2x 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
$$x^{2} - 35 = 2 x$$
to
$$- 2 x + \left(x^{2} - 35\right) = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = -35$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7$$
$$x_{2} = -5$$
left part with negative sign.
The equation is transformed from
$$x^{2} - 35 = 2 x$$
to
$$- 2 x + \left(x^{2} - 35\right) = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = -35$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-35) = 144
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7$$
$$x_{2} = -5$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -35$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -35$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -35$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -35$$
Sum and product of roots
[src]
sum
-5 + 7
$$-5 + 7$$
=
2
$$2$$
product
-5*7
$$- 35$$
=
-35
$$-35$$
-35
The graph