Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)=(-1/2)
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Equation sin(x-1)=0
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Equation sin(x)=-3/2
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Equation x+x/9=-10/3
- Express {x} in terms of y where:
- 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
- ((42^2-22)+(67*y))/67=((21^3-22)+(67*x))/67
- sqrt(1-x)^2+(4-y)^2=0
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Identical expressions
- y^ two +12y+ thirty-six = zero
- y squared plus 12y plus 36 equally 0
- y to the power of two plus 12y plus thirty minus six equally zero
- y2+12y+36=0
- y²+12y+36=0
- y to the power of 2+12y+36=0
- y^2+12y+36=O
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Similar expressions
- y^2+12y-36=0
- y^2-12y+36=0
y^2+12y+36=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 12$$
$$c = 36$$
, then
Because D = 0, then the equation has one root.
$$y_{1} = -6$$
a*y^2 + b*y + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 12$$
$$c = 36$$
, then
D = b^2 - 4 * a * c =
(12)^2 - 4 * (1) * (36) = 0
Because D = 0, then the equation has one root.
y = -b/2a = -12/2/(1)
$$y_{1} = -6$$
Vieta's Theorem
it is reduced quadratic equation
$$p y + q + y^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 12$$
$$q = \frac{c}{a}$$
$$q = 36$$
Vieta Formulas
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = -12$$
$$y_{1} y_{2} = 36$$
$$p y + q + y^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 12$$
$$q = \frac{c}{a}$$
$$q = 36$$
Vieta Formulas
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = -12$$
$$y_{1} y_{2} = 36$$