Standard Form of a Quadratic Equation
The standard form of a quadratic equation is [tex]Ax^2+Bx+C=0[/tex] where [tex]A, B,\ and\ C[/tex] are real numbers and [tex]A \neq 0[/tex].
[tex]A\ and\ B[/tex] are coefficients while [tex]C[/tex] is a constant.
To transform the equation, transpose the terms on the right side to the left side of the equation. While doing so, change their signs. If the term is originally positive, change it to negative. (This is a shortcut method called "transposing".)
[tex]-12x=3-5x^2\\\boxed{5x^2-12x-3=0}[/tex] [tex]\leftarrow[/tex] This is the standard form.
If you want to know the long method in solving this, see the solution below. This applies the additive inverse method.
[tex]-12x=3-5x^2\\5x^2 - 3 - 12x=\cancel{3+(-3)}\ \cancel{-\ 5x^2+(5x^2)}\\\text{Simplifying and arranging.}\\\bold{5x^2-12x-3=0}[/tex]
From the standard form, we can easily identify the values of [tex]A,\ B,\ and\ C[/tex].
[tex]A=5\\B=-12\\C=-3[/tex]
Happy learning!
