Solve the given quadratic equation by completing the square, $4 x^{2} - 20 x + 9 = 0$ .

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Solution

The given quadratic equation is $4 x^{2} - 20 x + 9 = 0$ .

Add and subtract $25$ in the equation $4 x^{2} - 20 x + 9 = 0$ to make a perfect square as shown below:

$4 x^{2} - 20 x + 9 = 0 \Rightarrow 4 x^{2} - 20 x + 25 - 25 + 9 = 0 \Rightarrow (2 x)^{2} - (2 \times 2 x \times 5) + 5^{2} + (- 25 + 9) = 0 \Rightarrow (2 x - 5)^{2} - 16 = 0 \Rightarrow (2 x - 5)^{2} = 16 \Rightarrow 2 x - 5 = \pm 4 \Rightarrow 2 x - 5 = - 4, 2 x - 5 = 4 \Rightarrow 2 x = 1, 2 x = 9 \Rightarrow x = \frac{1}{2}, x = \frac{9}{2}$

Hence, $x = \frac{1}{2}$ or $x = \frac{9}{2}$ .

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Solve the given quadratic equation by completing the square, 4x2−20x+9=0.

Solve the given quadratic equation by completing the square, $4 x^{2} - 20 x + 9 = 0$ .