Question

State the standard form of a quadratic equation in one variable. Solve method of perfect square.

Answer 1

Standard from of quadratic in one value

$a{x}^2+bx+c=0$

$\Rightarrow a{x}^2+bx+(\frac{b}{2\sqrt{a}}{)}^2-(\frac{b}{2\sqrt{a}})+c=0$

$\Rightarrow (\sqrt{a}x+\frac{b}{2\sqrt{a}}{)}^2-\frac{b^2}{4a}+c=0$

$\Rightarrow (\sqrt{a}x+\frac{b}{\sqrt{a}}{)}^2-(\sqrt{\frac{b^2-4ac}{4a}}{)}^2=0$

$\Rightarrow (\sqrt{ax}+\frac{b}{2\sqrt{a}}+\sqrt{\frac{b^{2}4ac}{4ac}})(\sqrt{a}x+\frac{b}{2\sqrt{a}}-\sqrt{\frac{b^2-4ac}{2a}})=0$

$\sqrt{ax}+\frac{b}{2\sqrt{a}}+\sqrt{\frac{b^2-4ac}{4a}}=0,\sqrt{ax}+\frac{b}{2\sqrt{a}}-\sqrt{\frac{b^2-4ac}{2a}}=c$

$x=\frac{-b+\sqrt{b^2-4ac}}{2\sqrt{a}.\sqrt{a}},x=\frac{-b-\sqrt{b^2-4ac}}{2\sqrt{a}.\sqrt{a}}$

$\therefore x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$