Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2/(x+6)=1/2
-
Equation 80-x=9*5
-
Equation 3x-2(3x-2)=19
-
Equation 8-3/5x=14
- Express {x} in terms of y where:
- -6*x+1*y=-5
- -5*x-2*y=9
- 1*x+11*y=-3
- 17*x-19*y=-12
-
Identical expressions
- (2x- twelve)*(x+ four)= zero
- (2x minus 12) multiply by (x plus 4) equally 0
- (2x minus twelve) multiply by (x plus four) equally zero
- (2x-12)(x+4)=0
- 2x-12x+4=0
- (2x-12)*(x+4)=O
-
Similar expressions
- (2x+12)*(x+4)=0
- (2x-12)*(x-4)=0
(2x-12)*(x+4)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x + 4\right) \left(2 x - 12\right) = 0$$
We get the quadratic equation
$$2 x^{2} - 4 x - 48 = 0$$
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
$$a = 2$$
$$b = -4$$
$$c = -48$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6$$
$$x_{2} = -4$$
$$\left(x + 4\right) \left(2 x - 12\right) = 0$$
We get the quadratic equation
$$2 x^{2} - 4 x - 48 = 0$$
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
$$a = 2$$
$$b = -4$$
$$c = -48$$
, then
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (2) * (-48) = 400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6$$
$$x_{2} = -4$$
Sum and product of roots
[src]
sum
-4 + 6
$$-4 + 6$$
=
2
$$2$$
product
-4*6
$$- 24$$
=
-24
$$-24$$
-24