Question

How do you factor this? x^{2} + 5 x- 9 = ?

Answer 1

$x^2+5x-9\\\\a=1;\ b=5;\ c=-9\\\Delta=b^2-4ac\\\\\Delta=5^2-4\cdot1\cdot(-9)=25+36=61 > 0\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{61}\\\\x_1=\dfrac{-5-\sqrt{61}}{2\cdot1}=\dfrac{-5-\sqrt{61}}{2}\\\\x_2=\dfrac{-5+\sqrt{61}}{2\cdot1}=\dfrac{-5+\sqrt{61}}{2}\\\\x^2+5x-9=\left(x-\dfrac{-5-\sqrt{61}}{2}\right)\left(x-\dfrac{-5+\sqrt{61}}{2}\right)$