Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4x-x^2=x^2-x+3
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Equation (x-4)/x=(2*x+10)/(x+4)
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Equation x+1/3=x-1/2
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Equation x-4=-2x+8
- Express {x} in terms of y where:
- -10*x+8*y=-12
- -20*x-20*y=-18
- -2*x-5*y=-12
- -3*x-13*y=-7
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Identical expressions
- (-4x- three)(3x+ zero , six)= zero
- ( minus 4x minus 3)(3x plus 0,6) equally 0
- ( minus 4x minus three)(3x plus zero , six) equally zero
- -4x-33x+0,6=0
- (-4x-3)(3x+0,6)=O
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Similar expressions
- (-4x+3)(3x+0,6)=0
- (4x-3)(3x+0,6)=0
- (-4x-3)(3x-0,6)=0
(-4x-3)(3x+0,6)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
(-4*x - 3)*(3*x + 3/5) = 0
$$\left(- 4 x - 3\right) \left(3 x + \frac{3}{5}\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(- 4 x - 3\right) \left(3 x + \frac{3}{5}\right) = 0$$
We get the quadratic equation
$$- 12 x^{2} - \frac{57 x}{5} - \frac{9}{5} = 0$$
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
$$a = -12$$
$$b = - \frac{57}{5}$$
$$c = - \frac{9}{5}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{3}{4}$$
$$x_{2} = - \frac{1}{5}$$
$$\left(- 4 x - 3\right) \left(3 x + \frac{3}{5}\right) = 0$$
We get the quadratic equation
$$- 12 x^{2} - \frac{57 x}{5} - \frac{9}{5} = 0$$
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
$$a = -12$$
$$b = - \frac{57}{5}$$
$$c = - \frac{9}{5}$$
, then
D = b^2 - 4 * a * c =
(-57/5)^2 - 4 * (-12) * (-9/5) = 1089/25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{3}{4}$$
$$x_{2} = - \frac{1}{5}$$
Rapid solution
[src]
x1 = -3/4
$$x_{1} = - \frac{3}{4}$$
x2 = -1/5
$$x_{2} = - \frac{1}{5}$$
x2 = -1/5
Sum and product of roots
[src]
sum
-3/4 - 1/5
$$- \frac{3}{4} - \frac{1}{5}$$
=
-19 ---- 20
$$- \frac{19}{20}$$
product
-3*(-1) ------- 4*5
$$- \frac{-3}{20}$$
=
3/20
$$\frac{3}{20}$$
3/20
The graph