Consider the function=$${\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{bx}}{\mathtt{\,\small\textbf+\,}}\left({\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{a}}\right)$$, where a,b are constant
change the function in the form$${{A}{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{B}}\right)}}^{\,{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{C}}$$ where A,B and C are constant
+130540 4x^2 - bx + (5 - a) we need to "complete the square," here.... first, factor out the 4...
4 [ x ^2 - (b/4) x + (5-a)/4] ...take (1/2) the coefficient on the x term, (b/8), square it, and add and subtract it
4[ x ^2 - (b/4)x + (b^2/64) + (5-a)/4 - (b^2/64)] =
4[(x - b/8)^2 + (16(5-a) - b^2)/64 ] =
4(x - b/8)^2 + [ (80 - 16a - b^2) / 16 ]
+130540 4x^2 - bx + (5 - a) we need to "complete the square," here.... first, factor out the 4...
4 [ x ^2 - (b/4) x + (5-a)/4] ...take (1/2) the coefficient on the x term, (b/8), square it, and add and subtract it
4[ x ^2 - (b/4)x + (b^2/64) + (5-a)/4 - (b^2/64)] =
4[(x - b/8)^2 + (16(5-a) - b^2)/64 ] =
4(x - b/8)^2 + [ (80 - 16a - b^2) / 16 ]
