If $\sqrt{1 + \frac{27}{169}} = \left(1 + \frac{x}{13}\right)$, then the value of x is

Explanation

## Page 44 $$ \sqrt{\left(1 + \frac{27}{169}\right)} = \left(1 + \frac{x}{13}\right) $$ $$ \sqrt{\left(\frac{169+27}{169}\right)} = 1 + \frac{x}{13} $$ $$ \sqrt{\frac{196}{169}} = 1 + \frac{x}{13} $$ $$ \frac{14}{13} = 1 + \frac{x}{13} \quad | \frac{-14}{13} = 1 + \frac{x}{13} $$ $$ 14 = 13 + x - 14 = 13 + x $$ $$ x = 1 \quad | \quad x = -27 $$ ## Decimal and Fraction