# Category: How Do

## How To Solve Arithmetic Sequences

Input interpretation arithmetic progression Alternate name arithmetic sequence Definition An arithmetic progression, also known as an arithmetic sequence, is a sequence of n numbers {a_0 + kd}_(k = 0)^(n – 1) such that the differences between successive terms is a constant d. An arithmetic progression can be generated in the Wolfram Language using the command […]

## How To Solve Complete The Square

Input interpretation complete the square | 28 + 10 x + x^2 Result (x + 5)^2 + 3 Geometric figure parabola Polynomial discriminant Delta = -12 Derivative d/dx((x + 5)^2 + 3) = 2 (x + 5) Indefinite integral integral (3 + (5 + x)^2) dx = x^3/3 + 5 x^2 + 28 x + […]

## How To Solve Completing The Square

Input interpretation complete the square | 28 + 10 x + x^2 Result (x + 5)^2 + 3 Geometric figure parabola Polynomial discriminant Delta = -12 Derivative d/dx((x + 5)^2 + 3) = 2 (x + 5) Indefinite integral integral (3 + (5 + x)^2) dx = x^3/3 + 5 x^2 + 28 x + […]

## How To Solve Each Equation

Input interpretation equation Definition An equation is a mathematical expression stating that two or more quantities are the same as one another, also called an equality, formula, or identity. Related topics algebraic equation | differential-algebraic equation | differential equation | Diophantine equation | equality | formula | identity | inequality | inequation | modular equation […]

## How To Solve Equations With Absolute Value

Input abs(x) Alternate form assuming x>0 x Alternate form assuming x is real sqrt(x^2) Root x = 0 Derivative d/dx(abs(x)) = x/abs(x) (assuming a function from reals to reals) Indefinite integral assuming all variables are real integral abs(x) dx = 1/2 x^2 sgn(x) + constant Global minimum min{abs(x)} = 0 at x = 0

## How To Solve For Slope

Input interpretation plane curve | Cartesian equation y = 1 + 3 x | x-intercept Result -1/3~~-0.333333 Geometric figure line Properties of line x-intercept | -1/3~~-0.333333 y-intercept | 1 slope | 3