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Lostsunrise [7]
3 years ago
7

2x2 - 4x –9 = 0 Completing the swuare

Mathematics
1 answer:
ASHA 777 [7]3 years ago
4 0

Step-by-step 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}\\\\\dfrac{2x^2}{2}-\dfrac{4x}{2}=\dfrac{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\sqrt{5.5}\qquad|\text{add 1 to both sides}\\\\x=1-\sqrt{5.5}\ \vee\ x=1+\sqrt{5.5}

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