Mister Exam
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How to use it?
- Equation:
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Equation x^2+x-4=0
-
Equation x^2=49
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Equation (x+6)^3=25*(x+6)
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Equation 1-5x=-6x+8
- Express {x} in terms of y where:
- 1*x-6*y=-19
- -1*x-20*y=-17
- 9*x+18*y=3
- 13*x-15*y=-6
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Identical expressions
- (one 5x- one)(6x+1, two)= zero
- (15x minus 1)(6x plus 1,2) equally 0
- (one 5x minus one)(6x plus 1, two) equally zero
- 15x-16x+1,2=0
- (15x-1)(6x+1,2)=O
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Similar expressions
- (15x+1)(6x+1,2)=0
- (15x-1)(6x-1,2)=0
(15x-1)(6x+1,2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
(15*x - 1)*(6*x + 6/5) = 0
$$\left(6 x + \frac{6}{5}\right) \left(15 x - 1\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(6 x + \frac{6}{5}\right) \left(15 x - 1\right) = 0$$
We get the quadratic equation
$$90 x^{2} + 12 x - \frac{6}{5} = 0$$
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
$$a = 90$$
$$b = 12$$
$$c = - \frac{6}{5}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{1}{15}$$
$$x_{2} = - \frac{1}{5}$$
$$\left(6 x + \frac{6}{5}\right) \left(15 x - 1\right) = 0$$
We get the quadratic equation
$$90 x^{2} + 12 x - \frac{6}{5} = 0$$
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
$$a = 90$$
$$b = 12$$
$$c = - \frac{6}{5}$$
, then
D = b^2 - 4 * a * c =
(12)^2 - 4 * (90) * (-6/5) = 576
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{15}$$
$$x_{2} = - \frac{1}{5}$$
Rapid solution
[src]
x1 = -1/5
$$x_{1} = - \frac{1}{5}$$
x2 = 1/15
$$x_{2} = \frac{1}{15}$$
x2 = 1/15
Sum and product of roots
[src]
sum
-1/5 + 1/15
$$- \frac{1}{5} + \frac{1}{15}$$
=
-2/15
$$- \frac{2}{15}$$
product
-1 ---- 5*15
$$- \frac{1}{75}$$
=
-1/75
$$- \frac{1}{75}$$
-1/75