Mister Exam
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How to use it?
- Equation:
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Equation cos(x)-1=0
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Equation (5*x+4)/2+3=9*x/4
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Equation 7*x^3-28*x=0
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Equation 4x+9=5(2x-7)-6x
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Identical expressions
- seven *x+ one /x+ four -(x- eleven)/x+ four = zero
- 7 multiply by x plus 1 divide by x plus 4 minus (x minus 11) divide by x plus 4 equally 0
- seven multiply by x plus one divide by x plus four minus (x minus eleven) divide by x plus four equally zero
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Similar expressions
- 7*x+1/x+4-(x+11)/x+4=0
- 7*x-1/x+4-(x-11)/x+4=0
- 7*x+1/x+4+(x-11)/x+4=0
- 7*x+1/x-4-(x-11)/x+4=0
- 7*x+1/x+4-(x-11)/x-4=0
7*x+1/x+4-(x-11)/x+4=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
1 x - 11
7*x + 1*- + 4 - ------ + 4 = 0
x x
$$7 x + 4 + 4 - \frac{x - 11}{x} + 1 \cdot \frac{1}{x} = 0$$
Detail solution
Given the equation:
$$7 x + 4 + 4 - \frac{x - 11}{x} + 1 \cdot \frac{1}{x} = 0$$
transform:
Take common factor from the equation
$$\frac{7 x^{2} + 7 x + 12}{x} = 0$$
the denominator
$$x$$
then
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$7 x^{2} + 7 x + 12 = 0$$
solve the resulting equation:
2.
$$7 x^{2} + 7 x + 12 = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 7$$
$$b = 7$$
$$c = 12$$
, then
$$D = b^2 - 4 * a * c = $$
$$\left(-1\right) 7 \cdot 4 \cdot 12 + 7^{2} = -287$$
Because D<0, then the equation
has no real roots,
but complex roots is exists.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = - \frac{1}{2} + \frac{\sqrt{287} i}{14}$$
Simplify
$$x_{2} = - \frac{1}{2} - \frac{\sqrt{287} i}{14}$$
Simplify
but
The final answer:
$$x_{1} = - \frac{1}{2} + \frac{\sqrt{287} i}{14}$$
$$x_{2} = - \frac{1}{2} - \frac{\sqrt{287} i}{14}$$
$$7 x + 4 + 4 - \frac{x - 11}{x} + 1 \cdot \frac{1}{x} = 0$$
transform:
Take common factor from the equation
$$\frac{7 x^{2} + 7 x + 12}{x} = 0$$
the denominator
$$x$$
then
x is not equal to 0
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$7 x^{2} + 7 x + 12 = 0$$
solve the resulting equation:
2.
$$7 x^{2} + 7 x + 12 = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 7$$
$$b = 7$$
$$c = 12$$
, then
$$D = b^2 - 4 * a * c = $$
$$\left(-1\right) 7 \cdot 4 \cdot 12 + 7^{2} = -287$$
Because D<0, then the equation
has no real roots,
but complex roots is exists.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = - \frac{1}{2} + \frac{\sqrt{287} i}{14}$$
Simplify
$$x_{2} = - \frac{1}{2} - \frac{\sqrt{287} i}{14}$$
Simplify
but
x is not equal to 0
The final answer:
$$x_{1} = - \frac{1}{2} + \frac{\sqrt{287} i}{14}$$
$$x_{2} = - \frac{1}{2} - \frac{\sqrt{287} i}{14}$$
Rapid solution
[src]
_____
1 I*\/ 287
x_1 = - - - ---------
2 14
$$x_{1} = - \frac{1}{2} - \frac{\sqrt{287} i}{14}$$
_____
1 I*\/ 287
x_2 = - - + ---------
2 14
$$x_{2} = - \frac{1}{2} + \frac{\sqrt{287} i}{14}$$
Sum and product of roots
[src]
sum
_____ _____ 1 I*\/ 287 1 I*\/ 287 - - - --------- + - - + --------- 2 14 2 14
$$\left(- \frac{1}{2} - \frac{\sqrt{287} i}{14}\right) + \left(- \frac{1}{2} + \frac{\sqrt{287} i}{14}\right)$$
=
-1
$$-1$$
product
_____ _____ 1 I*\/ 287 1 I*\/ 287 - - - --------- * - - + --------- 2 14 2 14
$$\left(- \frac{1}{2} - \frac{\sqrt{287} i}{14}\right) * \left(- \frac{1}{2} + \frac{\sqrt{287} i}{14}\right)$$
=
12/7
$$\frac{12}{7}$$
Numerical answer
[src]
x1 = -0.5 - 1.21007673900696*i
x2 = -0.5 + 1.21007673900696*i
x2 = -0.5 + 1.21007673900696*i
The graph