Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2-8=(x-4)^2
-
Equation 2,6x-0,75=0,9x-35,6
-
Equation (x+3)/3=(3-x)/8
-
Equation 36-x^2=0
- Express {x} in terms of y where:
- 8*x+5*y=-12
- -7*x-4*y=-4
- -2*x-10*y=20
- -1*x+11*y=16
-
Identical expressions
- (x+ six)*(- five *x- nine)= zero
- (x plus 6) multiply by ( minus 5 multiply by x minus 9) equally 0
- (x plus six) multiply by ( minus five multiply by x minus nine) equally zero
- (x+6)(-5x-9)=0
- x+6-5x-9=0
- (x+6)*(-5*x-9)=O
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Similar expressions
- (x+6)*(-5*x+9)=0
- (x+6)*(5*x-9)=0
- (x-6)*(-5*x-9)=0
(x+6)*(-5*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
$$\left(- 5 x - 9\right) \left(x + 6\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} - 39 x - 54 = 0$$
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
$$a = -5$$
$$b = -39$$
$$c = -54$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -6$$
$$x_{2} = - \frac{9}{5}$$
$$\left(- 5 x - 9\right) \left(x + 6\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} - 39 x - 54 = 0$$
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
$$a = -5$$
$$b = -39$$
$$c = -54$$
, then
D = b^2 - 4 * a * c =
(-39)^2 - 4 * (-5) * (-54) = 441
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -6$$
$$x_{2} = - \frac{9}{5}$$
Sum and product of roots
[src]
sum
-6 - 9/5
$$-6 - \frac{9}{5}$$
=
-39/5
$$- \frac{39}{5}$$
product
-6*(-9) ------- 5
$$- \frac{-54}{5}$$
=
54/5
$$\frac{54}{5}$$
54/5