Solve the following equations by using the method of completing t… - Vidyadip

Question

Solve the following equations by using the method of completing the square:
$x^2 + 8x - 2 = 0$

✓

Answer

$x^2 + 8x - 2 = 0$
$\Rightarrow x^2 + 8x = 2$
$\Rightarrow x^2 + 2 \times x \times 4 + 4^2 = 2 + 4^2$ (Adding $4^2$ on both sides)
$\Rightarrow (x + 4)^2= 2 + 16 = 18$
$\Rightarrow\text{x}+4=\pm\sqrt{18}=\pm3\sqrt2$ (Taking square root on both sides)
$\Rightarrow\text{x}+4=3\sqrt2$ or $\text{x}+4=-3\sqrt2$
$\Rightarrow\text{x}=-4+3\sqrt2$ or $\text{x}=-4-3\sqrt2$
Hence, $\big(-4+3\sqrt2\big)$ and $\big(-4-3\sqrt2\big)$ are the roots of the given equation.

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