Question

2x2 - 4x –9 = 0
Completing the swuare

Answer 1

Explanation:

`(a-b)^2=a^2-2ab+b^2\\\\2x^2-4x-9=0\qquad|\text{add 9 to both sides}\\\\2x^2-4x-9+9=0+9\\\\2x^2-4x=9\qquad|\text{divide both sides by 2}\\\\(2x^2)/(2)-(4x)/(2)=(9)/(2)\\\\x^2-2x=4.5\\\\x^2-2\cdot x\cdot1=4.5\qquad|\text{add}\ 1^2\ \text{to both sides}\\\\x^2-2\cdot x\cdot1+1^2=4.5+1^2\\\\(x-1)^2=5.5\iff x-1=\pm√(5.5)\qquad|\text{add 1 to both sides}\\\\x=1-√(5.5)\ \vee\ x=1+√(5.5)`