Remember that quadratic formula: [tex]x= \frac{-b(+/-) \sqrt{b^{2}-4ac} }{2a} [/tex] is used to solve quadratic equations of the form [tex]ax^{2}+bx+c[/tex].
Four our problem, the first one, [tex](x-1)^2=4[/tex], is not in the form [tex]ax^{2}+bx+c[/tex]. So is not a good idea to use the quadratic formula for this one.
The second one, [tex]0.25x^{2}+0.8x-8=0[/tex], is in the correct form. Notice that in this equation [tex]a=0.25[/tex], [tex]b=0.8[/tex], and [tex]c=-8[/tex]. It would be appropriate to use the quadratic formula to solve this one.
The third one, [tex]3x^{2}-4x=15[/tex], can be expressed as: [tex]3x^{2}-4x-15=0[/tex]. This equation is also in the correct form. Here [tex]a=3[/tex], [tex]b=-4[/tex], and [tex]c=-15[/tex]. It would be appropriate to use the quadratic formula to solve this one.
The fourth one, [tex](x-6)(x+6)=0[/tex], is not in the form [tex]ax^{2}+bx+c[/tex]. So is not a good idea to use the quadratic formula for this one.
We can conclude that you should use the quadratic formula to solve the second and third equations.
