Mister Exam
Other calculators
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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
- -2*x-9*y=1
- 3*x-1*y=5
- -6*x-9*y=-20
- Integral of d{x}:
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x^2-6x-7
- Graphing y =:
- x^2-6x-7
- Canonical form:
- x^2-6x-7
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Identical expressions
- x^ two -6x- seven = zero
- x squared minus 6x minus 7 equally 0
- x to the power of two minus 6x minus seven equally zero
- x2-6x-7=0
- x²-6x-7=0
- x to the power of 2-6x-7=0
- x^2-6x-7=O
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Similar expressions
- x^2-6x+7=0
- x^2+6x-7=0
x^2-6x-7=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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -6$$
$$c = -7$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7$$
$$x_{2} = -1$$
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
$$a = 1$$
$$b = -6$$
$$c = -7$$
, then
D = b^2 - 4 * a * c =
(-6)^2 - 4 * (1) * (-7) = 64
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7$$
$$x_{2} = -1$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = -7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = -7$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = -7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = -7$$
The graph