Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3x=2
-
Equation x^2+7x=18
-
Equation x^2-4x=0
-
Equation (y^4+4*y^2-12)/4=0
- Express {x} in terms of y where:
- 13*x-18*y=-17
- -7*x-19*y=-18
- 5*x+12*y=18
- -12*x-8*y=13
-
Identical expressions
- (-5x+ two)(-x- four)= zero
- ( minus 5x plus 2)( minus x minus 4) equally 0
- ( minus 5x plus two)( minus x minus four) equally zero
- -5x+2-x-4=0
- (-5x+2)(-x-4)=O
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Similar expressions
- (-5x+2)(x-4)=0
- (5x+2)(-x-4)=0
- (-5x-2)(-x-4)=0
- (-5x+2)(-x+4)=0
(-5x+2)(-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
$$\left(2 - 5 x\right) \left(- x - 4\right) + 0 = 0$$
We get the quadratic equation
$$5 x^{2} + 18 x - 8 = 0$$
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
$$a = 5$$
$$b = 18$$
$$c = -8$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{2}{5}$$
Simplify
$$x_{2} = -4$$
Simplify
$$\left(2 - 5 x\right) \left(- x - 4\right) + 0 = 0$$
We get the quadratic equation
$$5 x^{2} + 18 x - 8 = 0$$
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
$$a = 5$$
$$b = 18$$
$$c = -8$$
, then
D = b^2 - 4 * a * c =
(18)^2 - 4 * (5) * (-8) = 484
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{2}{5}$$
Simplify
$$x_{2} = -4$$
Simplify
Sum and product of roots
[src]
sum
0 - 4 + 2/5
$$\left(-4 + 0\right) + \frac{2}{5}$$
=
-18/5
$$- \frac{18}{5}$$
product
1*-4*2/5
$$1 \left(-4\right) \frac{2}{5}$$
=
-8/5
$$- \frac{8}{5}$$
-8/5
The graph