What are the four steps for solving an equation? Should any other factors be accounted for when solving an equation?
You should know that there are many forms of equations, each form having a particular way of solving.
Considering as example the linear equation `ax + b = 0` , you should solve it by isolating the term that contains x to the left side such that:
`ax = -b => x = -b/a`
Considering as example an equation that contains square root and the unknown is under the square root, you should solve the equation by raising to the square both sides of equal sign such that:
`sqrt(ax+b) = c => (sqrt(ax+b))^2 = c^2 => ax + b = c^2 => ax = c^2 - b => x = (c^2 - b)/a`
Considering as example a quadratic equation `ax^2 + bx + c = 0` , you should use quadratic formula, `x_(1,2) = (-b+-sqrt(b^2-4ac))/(2a)` , to find solutions.
The exponential and logarithmic equations may be solved using the properties of functions, exponential and logarithmic identities and substitutions that help for an exponential or logarithmic equation to be solved using algebraic methods.
Trigonometric equations may be solved using trigonometric identities and substitutions.