Which constant should be added and subtracted | vedclass

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Question

(B) To solve the quadratic equation $4x^{2} - \sqrt{3}x - 5 = 0$ by the method of completing the square,we first ensure the coefficient of $x^{2}$ is

Vedclass · Accepted Answer

$\frac{3}{16}$

Vedclass · Answer

(B) To solve the quadratic equation $4x^{2} - \sqrt{3}x - 5 = 0$ by the method of completing the square,we first ensure the coefficient of $x^{2}$ is $1$ or a perfect square. Here,$4x^{2} = (2x)^{2}$.We rewrite the equation as $(2x)^{2} - 2(2x)(\frac{\sqrt{3}}{4}) - 5 = 0$.To complete the square in the form $(a - b)^{2} = a^{2} - 2ab + b^{2}$,we identify $a = 2x$ and $b = \frac{\sqrt{3}}{4}$.The term to be added and subtracted is $b^{2} = (\frac{\sqrt{3}}{4})^{2} = \frac{3}{16}$.Thus,the constant is $\frac{3}{16}$.

Which constant should be added and subtracted to solve the quadratic equation $4x^{2} - \sqrt{3}x - 5 = 0$ by the method of completing the square?

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