Question

Solve the equation: x2 - 12x = -36

Answer 1

$x^2-12x=-36\ \ \ |add\ 36\ to\ both\ sides\\\\x^2-12x+36=0\\\\x^2-2x\cdot6+6^2=0\ \ |use\ (a-b)^2=a^2-2ab+b^2\\\\(x-6)^2=0\iff x-6=0\ \ \ |add\ 6\ to\ both\ sides\\\\\boxed{x=6}$

Answer 2

$In ~~Use ... \\ x^2 - 12x = -36\rightarrow (ax^2+bx + c = 0) \\ x^2 - 12x + 36 = 0 \\ \\a = 1 \\ b = - 12 \\ c = 36 \\ \\ Delta: \\ \Delta = b^2 - 4ac \\ \Delta = (-12)^2 - 4.1.36 \\ \Delta = 144 -144 \\ \Delta = 0\\ \\ Bhaskara: \\ \\ x = \frac{-b\pm \sqrt{\Delta} }{2a} \\ \\ x = \frac{-(-12)\pm \sqrt{0} }{2.1} \\ \\ x = \frac{12\pm0}{2} \\ \\ x' = \frac{12 + 0}{2} = \frac{12}{2} = 6 \\ \\ x'' = \frac{12 - 0}{2} = \frac{12}{2} = 6 \\ \\ S = \{6\}$