What should be subtracted from ${4 x}^{2} - 20 x + 30$ to make it a perfect square?

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Solution

$4 x^{2} - 20 x + 30$
By using the completing square method,
$\Rightarrow {(2 x)}^{2} - 2 \times 2 x \times 5 + 5^{2} - 5^{2} + 30$
$\Rightarrow {(2 x - 5)}^{2} - 25 + 30$
$\Rightarrow {(2 x - 5)}^{2} + 5$
$∴ 5$ should be subtracted to make it a perfect square.
$∴ {(2 x - 5)}^{2} + 5 - 5 = {(2 x - 5)}^{2}$

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