Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^3-7x+6=0
-
Equation 2x^2-x+3=0
-
Equation 3x^2+1=0
-
Equation 2x^2-5x=0
- Express {x} in terms of y where:
- -20*x+2*y=19
- 17*x-13*y=-4
- -20*x+5*y=3
- 16*x-18*y=15
-
Identical expressions
- |- twelve *x+ nineteen |= fourteen . six *x
- module of minus 12 multiply by x plus 19| equally 14.6 multiply by x
- module of minus twelve multiply by x plus nineteen | equally fourteen . six multiply by x
- |-12x+19|=14.6x
-
Similar expressions
- |+12*x+19|=14.6*x
- |-12*x-19|=14.6*x
|-12*x+19|=14.6*x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$12 x - 19 \geq 0$$
or
$$\frac{19}{12} \leq x \wedge x < \infty$$
we get the equation
$$- \frac{73 x}{5} + \left(12 x - 19\right) = 0$$
after simplifying we get
$$- \frac{13 x}{5} - 19 = 0$$
the solution in this interval:
$$x_{1} = - \frac{95}{13}$$
but x1 not in the inequality interval
2.
$$12 x - 19 < 0$$
or
$$-\infty < x \wedge x < \frac{19}{12}$$
we get the equation
$$- \frac{73 x}{5} + \left(19 - 12 x\right) = 0$$
after simplifying we get
$$19 - \frac{133 x}{5} = 0$$
the solution in this interval:
$$x_{2} = \frac{5}{7}$$
The final answer:
$$x_{1} = \frac{5}{7}$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$12 x - 19 \geq 0$$
or
$$\frac{19}{12} \leq x \wedge x < \infty$$
we get the equation
$$- \frac{73 x}{5} + \left(12 x - 19\right) = 0$$
after simplifying we get
$$- \frac{13 x}{5} - 19 = 0$$
the solution in this interval:
$$x_{1} = - \frac{95}{13}$$
but x1 not in the inequality interval
2.
$$12 x - 19 < 0$$
or
$$-\infty < x \wedge x < \frac{19}{12}$$
we get the equation
$$- \frac{73 x}{5} + \left(19 - 12 x\right) = 0$$
after simplifying we get
$$19 - \frac{133 x}{5} = 0$$
the solution in this interval:
$$x_{2} = \frac{5}{7}$$
The final answer:
$$x_{1} = \frac{5}{7}$$
Sum and product of roots
[src]
sum
5/7
$$\frac{5}{7}$$
=
5/7
$$\frac{5}{7}$$
product
5/7
$$\frac{5}{7}$$
=
5/7
$$\frac{5}{7}$$
5/7