Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 9^x-8*3^x-9=0
- Equation x+y=4
-
Equation 5x+8=-12
-
Equation x/9+x=-3
- Express {x} in terms of y where:
- 18*x+17*y=-14
- 16*x-17*y=-15
- -4*x-4*y=19
- 15*x+1*y=19
- Graphing y =:
- x^2+4x-4
-
Identical expressions
- x^ two + four x-4= zero
- x squared plus 4x minus 4 equally 0
- x to the power of two plus four x minus 4 equally zero
- x2+4x-4=0
- x²+4x-4=0
- x to the power of 2+4x-4=0
- x^2+4x-4=O
-
Similar expressions
- x^2+4x+4=0
- x^2-4x-4=0
x^2+4x-4=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
$$a = 1$$
$$b = 4$$
$$c = -4$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -2 + 2 \sqrt{2}$$
$$x_{2} = - 2 \sqrt{2} - 2$$
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
$$a = 1$$
$$b = 4$$
$$c = -4$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (1) * (-4) = 32
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -2 + 2 \sqrt{2}$$
$$x_{2} = - 2 \sqrt{2} - 2$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = -4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = -4$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = -4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = -4$$
Rapid solution
[src]
___ x1 = -2 + 2*\/ 2
$$x_{1} = -2 + 2 \sqrt{2}$$
___ x2 = -2 - 2*\/ 2
$$x_{2} = - 2 \sqrt{2} - 2$$
x2 = -2*sqrt(2) - 2
Sum and product of roots
[src]
sum
___ ___ -2 + 2*\/ 2 + -2 - 2*\/ 2
$$\left(- 2 \sqrt{2} - 2\right) + \left(-2 + 2 \sqrt{2}\right)$$
=
-4
$$-4$$
product
/ ___\ / ___\ \-2 + 2*\/ 2 /*\-2 - 2*\/ 2 /
$$\left(-2 + 2 \sqrt{2}\right) \left(- 2 \sqrt{2} - 2\right)$$
=
-4
$$-4$$
-4
The graph