Algebric Calculators

Algebric Equations Solver

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Quadratic Formula: $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
Factoring Quadratic: $a x^{2} + b x + c = 0$
Slope of a Line: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Distance Formula: $d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$
Midpoint Formula: $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$
Linear Equation: $y = m x + b$
Exponent Rules: $a^{m} \cdot a^{n} = a^{m + n}$
Logarithm Rules: $\log (a b) = \log a + \log b$
Arithmetic Sequence: $a_{n} = a_{1} + (n - 1) d$
Geometric Sequence: $a_{n} = a_{1} \cdot r^{n - 1}$
Sum of Arithmetic Series: $S_{n} = \frac{n}{2} (a_{1} + a_{n})$
Sum of Geometric Series: $S_{n} = a_{1} \frac{1 - r^{n}}{1 - r}$
Binomial Theorem: $(a + b)^{n} = \sum_{k = 0}^{n} (\binom{n}{k}) a^{n - k} b^{k}$
Factorial: $n! = n \cdot (n - 1) \cdot \dots \cdot 1$
Permutations: $P (n, k) = \frac{n!}{(n - k)!}$
Combinations: $C (n, k) = \frac{n!}{k! (n - k)!}$
Complex Number: $z = a + b i$
Modulus of Complex Number: $∣ z ∣ = \sqrt{a^{2} + b^{2}}$
Pythagorean Theorem: $a^{2} + b^{2} = c^{2}$
Absolute Value: $∣ x ∣ = {\begin{cases} x & if x \geq 0 \\ - x & if x < 0 \end{cases}$