Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sinx=1
-
Equation cosx=1/2
-
Equation sqrt(x)+1=x-1
-
Equation (x^2-x-1)/(x^2-2*x)=0
- Express {x} in terms of y where:
- xy^1=y+x*sin(y/x)
- sqrt(x)*sin(y/x)=0
- 12*10^(-30)-0,1884*10^12*x^2-y(0,3768*10^12*x+1,183152*10^12*x^3)+y^2(2,760688*10^24*x^2)=0=0
- (x^2+y^2)×(x+y-3)=2xy
- Graphing y =:
- x^2
- 1/2x+3
- Derivative of:
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x^2
- Integral of d{x}:
-
x^2
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1/2x+3
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Identical expressions
- x^ two = one /2x+ three
- x squared equally 1 divide by 2x plus 3
- x to the power of two equally one divide by 2x plus three
- x2=1/2x+3
- x²=1/2x+3
- x to the power of 2=1/2x+3
- x^2=1 divide by 2x+3
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Similar expressions
- x^2-9*x+14=0
- 4x^4+6*((2)^1/2)*x^3+5x^2+9*((2)^1/2)x+3,5=0
- x^2=1/2x-3
x^2=1/2x+3 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
$$x^{2} = \frac{x}{2} + 3$$
to
$$x^{2} + \left(- \frac{x}{2} - 3\right) = 0$$
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
$$a = 1$$
$$b = - \frac{1}{2}$$
$$c = -3$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = - \frac{3}{2}$$
left part with negative sign.
The equation is transformed from
$$x^{2} = \frac{x}{2} + 3$$
to
$$x^{2} + \left(- \frac{x}{2} - 3\right) = 0$$
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
$$a = 1$$
$$b = - \frac{1}{2}$$
$$c = -3$$
, then
D = b^2 - 4 * a * c =
(-1/2)^2 - 4 * (1) * (-3) = 49/4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = - \frac{3}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{1}{2}$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{1}{2}$$
$$x_{1} x_{2} = -3$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{1}{2}$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{1}{2}$$
$$x_{1} x_{2} = -3$$
Sum and product of roots
[src]
sum
2 - 3/2
$$- \frac{3}{2} + 2$$
=
1/2
$$\frac{1}{2}$$
product
2*(-3) ------ 2
$$\frac{\left(-3\right) 2}{2}$$
=
-3
$$-3$$
-3