Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+2)^2=(x-8)^2
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Equation -x=3
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Equation x^2+6*x+9=0
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Equation 12/(x+3)=-6/7
- Express {x} in terms of y where:
- -4*x+19*y=-13
- -5*x-6*y=-1
- -16*x-2*y=4
- -7*x+15*y=18
- Factor polynomial:
- x^2+6*x+9
-
Identical expressions
- x^ two + six *x+ nine = zero
- x squared plus 6 multiply by x plus 9 equally 0
- x to the power of two plus six multiply by x plus nine equally zero
- x2+6*x+9=0
- x²+6*x+9=0
- x to the power of 2+6*x+9=0
- x^2+6x+9=0
- x2+6x+9=0
- x^2+6*x+9=O
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Similar expressions
- x^2-6*x+9=0
- x^2+6*x-9=0
x^2+6*x+9=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
$$a = 1$$
$$b = 6$$
$$c = 9$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = -3$$
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
$$a = 1$$
$$b = 6$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (1) * (9) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -6/2/(1)
$$x_{1} = -3$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 9$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = 9$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 9$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = 9$$
The graph