Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x/12+x/8+x=-29/6
-
Equation x^2+7x-18=0
- Equation x-y+2=0
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Equation (x-11)*(-x+9)=0
- Express {x} in terms of y where:
- 13*x-18*y=-17
- 7*x+6*y=20
- -7*x-19*y=-18
- 5*x+12*y=18
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Identical expressions
- (x- eleven)*(-x+ nine)= zero
- (x minus 11) multiply by ( minus x plus 9) equally 0
- (x minus eleven) multiply by ( minus x plus nine) equally zero
- (x-11)(-x+9)=0
- x-11-x+9=0
- (x-11)*(-x+9)=O
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Similar expressions
- (x+11)*(-x+9)=0
- (x-11)*(x+9)=0
- (x-11)*(-x-9)=0
(x-11)*(-x+9)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(9 - x\right) \left(x - 11\right) = 0$$
We get the quadratic equation
$$- x^{2} + 20 x - 99 = 0$$
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
$$a = -1$$
$$b = 20$$
$$c = -99$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 9$$
$$x_{2} = 11$$
$$\left(9 - x\right) \left(x - 11\right) = 0$$
We get the quadratic equation
$$- x^{2} + 20 x - 99 = 0$$
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
$$a = -1$$
$$b = 20$$
$$c = -99$$
, then
D = b^2 - 4 * a * c =
(20)^2 - 4 * (-1) * (-99) = 4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 9$$
$$x_{2} = 11$$
Sum and product of roots
[src]
sum
9 + 11
$$9 + 11$$
=
20
$$20$$
product
9*11
$$9 \cdot 11$$
=
99
$$99$$
99
The graph