Question

solve by completing square method :-4x^2-20x+9=0

Answer 1

This method can be used or u can use quadratic formula method to verify the answer.

Answer 2

x = (-5+√34)/2,  (-5-√34)/2

Step-by-step explanation:

$-4x^2-20x+9=0$

$\implies -4(x^2+5x-\frac{9}{4})=0$

$\implies x^2+2\times\frac{5}{2}x+(\frac{5}{2})^2-(\frac{5}{2})^2-\frac{9}{4}=0$

$\implies (x+\frac{5}{2})^2-\frac{25}{4}-\frac{9}{4}=0$

$\implies (x+\frac{5}{2})^2-\frac{34}{4}=0$

$\implies x+\frac{5}{2}=\pm\sqrt{\frac{34}{4}}$

$\implies x+\frac{5}{2}=\pm\frac{\sqrt{34}}{2}}$

$\implies x=-\frac{5}{2}\pm\frac{\sqrt{34}}{2}}$

$\implies x=\frac{-5+\sqrt{34}}{2}, \frac{-5-\sqrt{34}}{2}$

Hope this answer is helpful.

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