Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation -x^2+6*x-7=0
-
Equation -x^3+4*x^2+4*x-16=0
-
Equation x/7=6
-
Equation 2x-cosx=0
- Express {x} in terms of y where:
- 13*x-12*y=10
- -12*x-19*y=16
- 4*x-7*y=11
- 18*x-11*y=13
- Sum of series:
-
22
- Expression:
- 22
-
Identical expressions
- five |4x- eight |+ seven , six = twenty-two
- 5 module of 4x minus 8| plus 7,6 equally 22
- five module of 4x minus eight | plus seven , six equally twenty minus two
-
Similar expressions
- log1/2(2x-6)=-2
- 5|4x+8|+7,6=22
- (x-3)^2=(x+2)^2
- 5|4x-8|-7,6=22
- (x-2)^2=3
5|4x-8|+7,6=22 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.
$$4 x - 8 \geq 0$$
or
$$2 \leq x \wedge x < \infty$$
we get the equation
$$5 \left(4 x - 8\right) - \frac{72}{5} = 0$$
after simplifying we get
$$20 x - \frac{272}{5} = 0$$
the solution in this interval:
$$x_{1} = \frac{68}{25}$$
2.
$$4 x - 8 < 0$$
or
$$-\infty < x \wedge x < 2$$
we get the equation
$$5 \left(8 - 4 x\right) - \frac{72}{5} = 0$$
after simplifying we get
$$\frac{128}{5} - 20 x = 0$$
the solution in this interval:
$$x_{2} = \frac{32}{25}$$
The final answer:
$$x_{1} = \frac{68}{25}$$
$$x_{2} = \frac{32}{25}$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$4 x - 8 \geq 0$$
or
$$2 \leq x \wedge x < \infty$$
we get the equation
$$5 \left(4 x - 8\right) - \frac{72}{5} = 0$$
after simplifying we get
$$20 x - \frac{272}{5} = 0$$
the solution in this interval:
$$x_{1} = \frac{68}{25}$$
2.
$$4 x - 8 < 0$$
or
$$-\infty < x \wedge x < 2$$
we get the equation
$$5 \left(8 - 4 x\right) - \frac{72}{5} = 0$$
after simplifying we get
$$\frac{128}{5} - 20 x = 0$$
the solution in this interval:
$$x_{2} = \frac{32}{25}$$
The final answer:
$$x_{1} = \frac{68}{25}$$
$$x_{2} = \frac{32}{25}$$
Rapid solution
[src]
32
x1 = --
25
$$x_{1} = \frac{32}{25}$$
68
x2 = --
25
$$x_{2} = \frac{68}{25}$$
x2 = 68/25
Sum and product of roots
[src]
sum
32 68 -- + -- 25 25
$$\frac{32}{25} + \frac{68}{25}$$
=
4
$$4$$
product
32*68 ----- 25*25
$$\frac{32 \cdot 68}{25 \cdot 25}$$
=
2176 ---- 625
$$\frac{2176}{625}$$
2176/625