Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 9x−9(x+1)=−2x
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Equation -25-x=-17
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Equation -x^2+5*x-6=0
- Equation x-y=7
- Express {x} in terms of y where:
- 7*x-1*y=-7
- 10*x-15*y=16
- 10*x-18*y=3
- 19*x-12*y=16
- Graphing y =:
- -x^2+5*x-6
- Integral of d{x}:
- -x^2+5*x-6
-
Identical expressions
- -x^ two + five *x- six = zero
- minus x squared plus 5 multiply by x minus 6 equally 0
- minus x to the power of two plus five multiply by x minus six equally zero
- -x2+5*x-6=0
- -x²+5*x-6=0
- -x to the power of 2+5*x-6=0
- -x^2+5x-6=0
- -x2+5x-6=0
- -x^2+5*x-6=O
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Similar expressions
- -x^2-5*x-6=0
- -x^2+5*x+6=0
- x^2+5*x-6=0
-x^2+5*x-6=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
$$a = -1$$
$$b = 5$$
$$c = -6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = 3$$
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
$$a = -1$$
$$b = 5$$
$$c = -6$$
, then
D = b^2 - 4 * a * c =
(5)^2 - 4 * (-1) * (-6) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = 3$$
Vieta's Theorem
rewrite the equation
$$\left(- x^{2} + 5 x\right) - 6 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 5 x + 6 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = 6$$
$$\left(- x^{2} + 5 x\right) - 6 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 5 x + 6 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = 6$$
The graph