Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+3*x+9=0
-
Equation x^2+3*x+2=0
-
Equation 3*x=28-x
-
Equation (x-3)(x-7)=21
- Express {x} in terms of y where:
- 9*x-8*y=-6
- -11*x+1*y=-14
- 7*x-17*y=2
- -13*x+15*y=1
- Derivative of:
-
-x^2
- Graphing y =:
- -x^2
- Limit of the function:
-
-x^2
-
Identical expressions
- 16x+ sixty-four =-x^ two
- 16x plus 64 equally minus x squared
- 16x plus sixty minus four equally minus x to the power of two
- 16x+64=-x2
- 16x+64=-x²
- 16x+64=-x to the power of 2
-
Similar expressions
- (x-1)^3-x^2*(x-4)-(x+2)*(x-2)=0
- -(x^2-16*x+64)=64
- 16x-64=-x^2
- 16x+64=+x^2
16x+64=-x^2 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
$$16 x + 64 = - x^{2}$$
to
$$x^{2} + \left(16 x + 64\right) = 0$$
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
$$a = 1$$
$$b = 16$$
$$c = 64$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = -8$$
left part with negative sign.
The equation is transformed from
$$16 x + 64 = - x^{2}$$
to
$$x^{2} + \left(16 x + 64\right) = 0$$
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
$$a = 1$$
$$b = 16$$
$$c = 64$$
, then
D = b^2 - 4 * a * c =
(16)^2 - 4 * (1) * (64) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -16/2/(1)
$$x_{1} = -8$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 16$$
$$q = \frac{c}{a}$$
$$q = 64$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -16$$
$$x_{1} x_{2} = 64$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 16$$
$$q = \frac{c}{a}$$
$$q = 64$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -16$$
$$x_{1} x_{2} = 64$$
The graph