+4 hello friend, for a quadratic equation is solved by three methods ; complementation of the square, by the factorization and the general formula, in particular need a method ?
+9665 For me, I usually use factorization or quadratic formula.
Factorization example:
\(x(x-5)=-4\\ x^2-5x+4=0\\ \color{red}(x-1)\color{aqua}(x-4)\color{black}=0\\ \text{Set each factor to 0.}\\ \color{red}x-1=0\\ \mathbf{\color{red}x=1}\\ \color{aqua}x-4=0\\ \mathbf{\color{aqua}x=4}\\ \therefore \color{red}x=1 \color{black} \text{ and } \color{aqua}x=4 \)
Quadratic formula example:
\(x^2-x-1=0\\ x=\dfrac{-(-1)\pm\sqrt{(-1)^2-(4)(1)(-1)}}{2(1)}\\ \;\;=\dfrac{1\pm\sqrt5}{2}\\ \therefore x=\dfrac{1+\sqrt5}{2}\text{ and }x=\dfrac{1-\sqrt5}{2}\)
\(\text{Just for you to know: The solution of }ax^2+bx+c=0\\\text{ is }x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
Complementation of the square example: (I usually call it completing the square)
\(x^2+8x+15=0\\ x^2+8x+16-1=0\\ (x+4)^2=1\\ x+4=\pm \sqrt1\\ \;\;\;\;\;\;\;\;\;\!=\pm 1\\ x= -3\text{ and }x=-5\)
