Solution:
Consider the following equation:
[tex]x^2-12x=-27[/tex]this is equivalent to the following quadratic equation:
[tex]x^2-12x+27=0[/tex]
to solve this quadratic equation, we can apply the following quadratic formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]here,
a = 1
b = -12
and
c = 27
so that, the solutions to the given quadratic equation are:
[tex]x_1\text{ = }\frac{12+\sqrt[]{(-12)^2-4(1)(27)}}{2(1)}=\frac{12+\sqrt[]{36}}{2}=\frac{12+6}{2}=9[/tex]and
[tex]x_2\text{ = }\frac{12-\sqrt[]{(-12)^2-4(1)(27)}}{2(1)}\text{ =}\frac{12-\sqrt[]{36}}{2}\text{= }\frac{12-6}{2}=3[/tex]So that, the correct answer is:
the solutions are:
9 and 3.
