Question
Solve the following equations by using the method of completing the square:
$\text{4x}^2+4\sqrt3+3=0$
$\text{4x}^2+4\sqrt3+3=0$
✓
Answer
$\text{4x}^2+4\sqrt3+3=0$
$\Rightarrow\text{4x}^2+4\sqrt3\text{x}=-3$
$\Rightarrow(\text{2x})^2+2\times\text{2x}\times\sqrt3+\big(\sqrt3\big)^2\\=-3+\big(\sqrt3\big)^2$ $[$ Adding $\big(\sqrt3\big)^2$ on Both sides$]$
$\Rightarrow\big(\text{2x}+\sqrt3\big)^2=-3+3=0$
$\Rightarrow\text{2x}+\sqrt3=0$
$\Rightarrow\text{x}=-\frac{\sqrt3}{2}$
Hence, $-\frac{\sqrt3}2{}$ is the required root of the given equation.
$\Rightarrow\text{4x}^2+4\sqrt3\text{x}=-3$
$\Rightarrow(\text{2x})^2+2\times\text{2x}\times\sqrt3+\big(\sqrt3\big)^2\\=-3+\big(\sqrt3\big)^2$ $[$ Adding $\big(\sqrt3\big)^2$ on Both sides$]$
$\Rightarrow\big(\text{2x}+\sqrt3\big)^2=-3+3=0$
$\Rightarrow\text{2x}+\sqrt3=0$
$\Rightarrow\text{x}=-\frac{\sqrt3}{2}$
Hence, $-\frac{\sqrt3}2{}$ is the required root of the given equation.
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