Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+11*x+30=0
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Equation x²-6x+5=0
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Equation 2x+4=6
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Equation 4^x+3=11^x
- Express {x} in terms of y where:
- -20*x+5*y=13
- -10*x+8*y=-12
- -20*x-20*y=-18
- 9*x+9*y=18
- Graphing y =:
- e^x
- Integral of d{x}:
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e^x
- Derivative of:
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e^x
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Identical expressions
- e^x=2x+ one / three
- e to the power of x equally 2x plus 1 divide by 3
- e to the power of x equally 2x plus one divide by three
- ex=2x+1/3
- e^x=2x+1 divide by 3
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Similar expressions
- (2x+1)/3+(10-3x)/2=2
- e^x=2x-1/3
e^x=2x+1/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Sum and product of roots
[src]
sum
/ / -1/6 \\ / / -1/6 \\ 1 | |-e || | |-e || - - - re|W|-------|| - I*im|W|-------|| 6 \ \ 2 // \ \ 2 //
$$- \frac{1}{6} - \operatorname{re}{\left(W\left(- \frac{1}{2 e^{\frac{1}{6}}}\right)\right)} - i \operatorname{im}{\left(W\left(- \frac{1}{2 e^{\frac{1}{6}}}\right)\right)}$$
=
/ / -1/6 \\ / / -1/6 \\ 1 | |-e || | |-e || - - - re|W|-------|| - I*im|W|-------|| 6 \ \ 2 // \ \ 2 //
$$- \frac{1}{6} - \operatorname{re}{\left(W\left(- \frac{1}{2 e^{\frac{1}{6}}}\right)\right)} - i \operatorname{im}{\left(W\left(- \frac{1}{2 e^{\frac{1}{6}}}\right)\right)}$$
product
/ / -1/6 \\ / / -1/6 \\ 1 | |-e || | |-e || - - - re|W|-------|| - I*im|W|-------|| 6 \ \ 2 // \ \ 2 //
$$- \frac{1}{6} - \operatorname{re}{\left(W\left(- \frac{1}{2 e^{\frac{1}{6}}}\right)\right)} - i \operatorname{im}{\left(W\left(- \frac{1}{2 e^{\frac{1}{6}}}\right)\right)}$$
=
/ / -1/6 \\ / / -1/6 \\ 1 | |-e || | |-e || - - - re|W|-------|| - I*im|W|-------|| 6 \ \ 2 // \ \ 2 //
$$- \frac{1}{6} - \operatorname{re}{\left(W\left(- \frac{1}{2 e^{\frac{1}{6}}}\right)\right)} - i \operatorname{im}{\left(W\left(- \frac{1}{2 e^{\frac{1}{6}}}\right)\right)}$$
-1/6 - re(LambertW(-exp(-1/6)/2)) - i*im(LambertW(-exp(-1/6)/2))
Rapid solution
[src]
/ / -1/6 \\ / / -1/6 \\
1 | |-e || | |-e ||
x1 = - - - re|W|-------|| - I*im|W|-------||
6 \ \ 2 // \ \ 2 //
$$x_{1} = - \frac{1}{6} - \operatorname{re}{\left(W\left(- \frac{1}{2 e^{\frac{1}{6}}}\right)\right)} - i \operatorname{im}{\left(W\left(- \frac{1}{2 e^{\frac{1}{6}}}\right)\right)}$$
x1 = -1/6 - re(LambertW(-exp(-1/6)/2)) - i*im(LambertW(-exp(-1/6)/2))
Numerical answer
[src]
x1 = 0.73958348997522 - 0.52538804877793*i
x1 = 0.73958348997522 - 0.52538804877793*i