Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 9-4x=3x-40
-
Equation x+4=0
-
Equation x^2+6x+9=0
-
Equation (x-2)^5+(4-x)^5=2
- Express {x} in terms of y where:
- 18*x+12*y=18
- -20*x-13*y=15
- 12*x-3*y=-2
- 17*x+1*y=-11
-
Identical expressions
- (x- three)*(x+ four)- eighteen = zero
- (x minus 3) multiply by (x plus 4) minus 18 equally 0
- (x minus three) multiply by (x plus four) minus eighteen equally zero
- (x-3)(x+4)-18=0
- x-3x+4-18=0
- (x-3)*(x+4)-18=O
-
Similar expressions
- (x-3)*(x-4)-18=0
- (x+3)*(x+4)-18=0
- (x-3)*(x+4)+18=0
(x-3)*(x+4)-18=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 3\right) \left(x + 4\right) - 18 = 0$$
We get the quadratic equation
$$x^{2} + x - 30 = 0$$
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
$$a = 1$$
$$b = 1$$
$$c = -30$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
$$x_{2} = -6$$
$$\left(x - 3\right) \left(x + 4\right) - 18 = 0$$
We get the quadratic equation
$$x^{2} + x - 30 = 0$$
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
$$a = 1$$
$$b = 1$$
$$c = -30$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (1) * (-30) = 121
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 5$$
$$x_{2} = -6$$
Sum and product of roots
[src]
sum
-6 + 5
$$-6 + 5$$
=
-1
$$-1$$
product
-6*5
$$- 30$$
=
-30
$$-30$$
-30
The graph