An equation is said to be reducible to quadratic (or quadratic form) if the variable factor of the leading term is the square of the variable factor in the second variable term. For example, look at the equation, \(a{x^6} + b{x^3} + c = 0\), this equation is not quadratic, but this can be made quadratic assuming \({x^3} = t\), and thus the equation reduces to \(at^2+bt+c=0\), which can be solved easily in \(t\).

These types of equations if we make an appropriate substitution to make them appear quadratic. 

To solve equations of quadratic form:

• Make an appropriate substitution so that the equation can be reduced to a quadratic equation. (Make sure you note what substitution you have made.)
• Solve the quadratic equation obtained in step 1.
• Use the values obtained in step 2 to obtain the values of the original variable you were asked to solve for.
• Check your answers in the original equation. Discard any solutions which do not make true equations.
• Some of the useful algebraic formulae can be used.