Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 13/(x-4)=2
-
Equation x/4+x=4
-
Equation x^2+11=0
- Equation x+y=5
- Express {x} in terms of y where:
- 6*x+17*y=-11
- -12*x-10*y=-16
- 15*x+10*y=-4
- 15*x+9*y=5
-
Identical expressions
- (x- six)(4x- six)= zero
- (x minus 6)(4x minus 6) equally 0
- (x minus six)(4x minus six) equally zero
- x-64x-6=0
- (x-6)(4x-6)=O
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Similar expressions
- (x-6)*(4x-6)=0
- (x-6)*(4*x-6)=0
- (x+6)(4x-6)=0
- (x-6)(4x+6)=0
(x-6)(4x-6)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 6\right) \left(4 x - 6\right) = 0$$
We get the quadratic equation
$$4 x^{2} - 30 x + 36 = 0$$
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
$$a = 4$$
$$b = -30$$
$$c = 36$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6$$
$$x_{2} = \frac{3}{2}$$
$$\left(x - 6\right) \left(4 x - 6\right) = 0$$
We get the quadratic equation
$$4 x^{2} - 30 x + 36 = 0$$
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
$$a = 4$$
$$b = -30$$
$$c = 36$$
, then
D = b^2 - 4 * a * c =
(-30)^2 - 4 * (4) * (36) = 324
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6$$
$$x_{2} = \frac{3}{2}$$
Sum and product of roots
[src]
sum
6 + 3/2
$$\frac{3}{2} + 6$$
=
15/2
$$\frac{15}{2}$$
product
6*3 --- 2
$$\frac{3 \cdot 6}{2}$$
=
9
$$9$$
9
The graph