Mister Exam
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How to use it?
- Equation:
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Equation x^4=(3x-10)^2
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Equation 7x-3=2x+1
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Equation x^2-9*x=0
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Equation (x-5)(2x+8)=0
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Identical expressions
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Similar expressions
- (x−14,9)⋅(9,8-2x)=0
(x−14,9)⋅(9,8+2x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ 149\ |x - ---|*(49/5 + 2*x) = 0 \ 10/
$$\left(x - \frac{149}{10}\right) \left(2 x + \frac{49}{5}\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(x - \frac{149}{10}\right) \left(2 x + \frac{49}{5}\right) = 0$$
We get the quadratic equation
$$2 x^{2} - 20 x - \frac{7301}{50} = 0$$
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
$$a = 2$$
$$b = -20$$
$$c = - \frac{7301}{50}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{149}{10}$$
$$x_{2} = - \frac{49}{10}$$
$$\left(x - \frac{149}{10}\right) \left(2 x + \frac{49}{5}\right) = 0$$
We get the quadratic equation
$$2 x^{2} - 20 x - \frac{7301}{50} = 0$$
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
$$a = 2$$
$$b = -20$$
$$c = - \frac{7301}{50}$$
, then
D = b^2 - 4 * a * c =
(-20)^2 - 4 * (2) * (-7301/50) = 39204/25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{149}{10}$$
$$x_{2} = - \frac{49}{10}$$
Sum and product of roots
[src]
sum
49 149 - -- + --- 10 10
$$- \frac{49}{10} + \frac{149}{10}$$
=
10
$$10$$
product
-49*149 ------- 10*10
$$- \frac{7301}{100}$$
=
-7301 ------ 100
$$- \frac{7301}{100}$$
-7301/100
Rapid solution
[src]
-49
x1 = ----
10
$$x_{1} = - \frac{49}{10}$$
149
x2 = ---
10
$$x_{2} = \frac{149}{10}$$
x2 = 149/10