Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)=-2
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Equation 17x-8=20x+7
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Equation 9*(x-5)=-x
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Equation x^2+2x-3=0
- Express {x} in terms of y where:
- 7*x+19*y=12
- 2*x+2*y=-6
- 10*x-2*y=0
- -9*x-4*y=-20
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Identical expressions
- (5x+ two)(-x- four)= zero
- (5x plus 2)( minus x minus 4) equally 0
- (5x plus two)( minus x minus four) equally zero
- 5x+2-x-4=0
- (5x+2)(-x-4)=O
-
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
(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
$$\left(- x - 4\right) \left(5 x + 2\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} - 22 x - 8 = 0$$
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
$$a = -5$$
$$b = -22$$
$$c = -8$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -4$$
$$x_{2} = - \frac{2}{5}$$
$$\left(- x - 4\right) \left(5 x + 2\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} - 22 x - 8 = 0$$
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
$$a = -5$$
$$b = -22$$
$$c = -8$$
, then
D = b^2 - 4 * a * c =
(-22)^2 - 4 * (-5) * (-8) = 324
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -4$$
$$x_{2} = - \frac{2}{5}$$
Sum and product of roots
[src]
sum
-4 - 2/5
$$-4 - \frac{2}{5}$$
=
-22/5
$$- \frac{22}{5}$$
product
-4*(-2) ------- 5
$$- \frac{-8}{5}$$
=
8/5
$$\frac{8}{5}$$
8/5
The graph