Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 5^x=8^x
-
Equation -27x+220=-5x
-
Equation x+12=5
-
Equation 3/(x-5)+8/x=2
- Express {x} in terms of y where:
- 12*x+1*y=15
- -16*x-10*y=4
- -4*x-20*y=10
- 19*x+6*y=8
-
Identical expressions
- (x- six)*(- five *x- nine)= zero
- (x minus 6) multiply by ( minus 5 multiply by x minus 9) equally 0
- (x minus 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
$$- 5 x^{2} + 21 x + 54 = 0$$
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
$$a = -5$$
$$b = 21$$
$$c = 54$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{9}{5}$$
$$x_{2} = 6$$
$$\left(- 5 x - 9\right) \left(x - 6\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} + 21 x + 54 = 0$$
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
$$a = -5$$
$$b = 21$$
$$c = 54$$
, then
D = b^2 - 4 * a * c =
(21)^2 - 4 * (-5) * (54) = 1521
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{9}{5}$$
$$x_{2} = 6$$
Sum and product of roots
[src]
sum
6 - 9/5
$$- \frac{9}{5} + 6$$
=
21/5
$$\frac{21}{5}$$
product
6*(-9) ------ 5
$$\frac{\left(-9\right) 6}{5}$$
=
-54/5
$$- \frac{54}{5}$$
-54/5