What constant number must be added or subtracted to $4 x^{2} + 12 x + 8 = 0$ to solve it by method of completing the square?

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Solution

Consider the given equation,

$4 x^{2} + 12 x + 8 = 0$

$x^{2} + 3 x + 2 = 0$ ..... (1)

Add and subtract ${(\frac{3}{2})}^{2}$ in equation (1), we get

$x^{2} + 3 x + 2 + {(\frac{3}{2})}^{2} - {(\frac{3}{2})}^{2} = 0$

${(x + \frac{3}{2})}^{2} + 2 - \frac{9}{4} = 0$

${(x + \frac{3}{2})}^{2} - \frac{1}{4} = 0$

Hence, need to add $\frac{1}{4}$ so that $x^{2} + 3 x + 2 = 0$ become a perfect square.

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What constant number must be added or subtracted to 4x2+12x+8=0 to solve it by method of completing the square?

Consider the given equation, 4x2+12x+8=0 x2+3x+2=0 ..... (1) Add and subtract (32)2 in equation (1), we get x2+3x+2+(32)2−(32)2=0 (x+32)2+2−94=0 (x+32)2−14=0 Hence, need to add 14 so that x2+3x+2=0 become a perfect square.

What constant number must be added or subtracted to $4 x^{2} + 12 x + 8 = 0$ to solve it by method of completing the square?