Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+7*x+12=0
-
Equation 12/x=3
-
Equation 7x-9=40
-
Equation (x-2)^2=(x-8)^2
- Express {x} in terms of y where:
- -6*x-11*y=-20
- -15*x+7*y=1
- -1*x-20*y=1
- -1*x-15*y=13
- Integral of d{x}:
- 105
- Canonical form:
- 105
-
Identical expressions
- (x- seventeen)(x- nine)= one hundred and five
- (x minus 17)(x minus 9) equally 105
- (x minus seventeen)(x minus nine) equally one hundred and five
- x-17x-9=105
-
Similar expressions
- x+5/6x+9/10*(5/6x)+8+9/10*5/6x=152
- (x-17)(x+9)=105
- 0,460-0,0035*(1,95*10^5)*(400*10^(-6))*((x-0,058)/x)+435*(327,6*10^(-6))=19*0,17*0,8*x
- (x+17)(x-9)=105
(x-17)(x-9)=105 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(x - 17\right) \left(x - 9\right) = 105$$
to
$$\left(x - 17\right) \left(x - 9\right) - 105 = 0$$
Expand the expression in the equation
$$\left(x - 17\right) \left(x - 9\right) - 105 = 0$$
We get the quadratic equation
$$x^{2} - 26 x + 48 = 0$$
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
$$a = 1$$
$$b = -26$$
$$c = 48$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 24$$
$$x_{2} = 2$$
left part with negative sign.
The equation is transformed from
$$\left(x - 17\right) \left(x - 9\right) = 105$$
to
$$\left(x - 17\right) \left(x - 9\right) - 105 = 0$$
Expand the expression in the equation
$$\left(x - 17\right) \left(x - 9\right) - 105 = 0$$
We get the quadratic equation
$$x^{2} - 26 x + 48 = 0$$
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
$$a = 1$$
$$b = -26$$
$$c = 48$$
, then
D = b^2 - 4 * a * c =
(-26)^2 - 4 * (1) * (48) = 484
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 24$$
$$x_{2} = 2$$
Sum and product of roots
[src]
sum
2 + 24
$$2 + 24$$
=
26
$$26$$
product
2*24
$$2 \cdot 24$$
=
48
$$48$$
48