Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2-2x-15=0
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Equation x^3+4x^2-9x-36=0
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Equation sqrt((3x+2)/(2x-3))+sqrt((2x-3)/(3x+2))=2,5
- Equation (y^3+4y^2-6)-(5y-y^3+6)=2y^3+4y^2+y
- Express {x} in terms of y where:
- 4*x-16*y=6
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
- 10*x-1*y=10
- 15*x-17*y=19
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Identical expressions
- |x^ two +7x|=4x+ ten
- module of x squared plus 7x| equally 4x plus 10
- module of x to the power of two plus 7x| equally 4x plus ten
- |x2+7x|=4x+10
- |x²+7x|=4x+10
- |x to the power of 2+7x|=4x+10
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Similar expressions
- 4(x+10)=-1
- |x^2+7x|=4x-10
- |x^2-7x|=4x+10
- (100-14)/14*x+(100-(3/1000))/(3/1000)*x=0
- p^2+320.44*x+109126.98=0
|x^2+7x|=4x+10 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.
$$x^{2} + 7 x \geq 0$$
or
$$\left(0 \leq x \wedge x < \infty\right) \vee \left(x \leq -7 \wedge -\infty < x\right)$$
we get the equation
$$- 4 x + \left(x^{2} + 7 x\right) - 10 = 0$$
after simplifying we get
$$x^{2} + 3 x - 10 = 0$$
the solution in this interval:
$$x_{1} = -5$$
but x1 not in the inequality interval
$$x_{2} = 2$$
2.
$$x^{2} + 7 x < 0$$
or
$$-7 < x \wedge x < 0$$
we get the equation
$$- 4 x + \left(- x^{2} - 7 x\right) - 10 = 0$$
after simplifying we get
$$- x^{2} - 11 x - 10 = 0$$
the solution in this interval:
$$x_{3} = -10$$
but x3 not in the inequality interval
$$x_{4} = -1$$
The final answer:
$$x_{1} = 2$$
$$x_{2} = -1$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x^{2} + 7 x \geq 0$$
or
$$\left(0 \leq x \wedge x < \infty\right) \vee \left(x \leq -7 \wedge -\infty < x\right)$$
we get the equation
$$- 4 x + \left(x^{2} + 7 x\right) - 10 = 0$$
after simplifying we get
$$x^{2} + 3 x - 10 = 0$$
the solution in this interval:
$$x_{1} = -5$$
but x1 not in the inequality interval
$$x_{2} = 2$$
2.
$$x^{2} + 7 x < 0$$
or
$$-7 < x \wedge x < 0$$
we get the equation
$$- 4 x + \left(- x^{2} - 7 x\right) - 10 = 0$$
after simplifying we get
$$- x^{2} - 11 x - 10 = 0$$
the solution in this interval:
$$x_{3} = -10$$
but x3 not in the inequality interval
$$x_{4} = -1$$
The final answer:
$$x_{1} = 2$$
$$x_{2} = -1$$