Answer: x ≈ −0.13 and x ≈ 1.53
Step-by-step explanation:
Here, the given equation is,
\(5x^2-7x=1\)
\(\implies x^2 - \frac{7}{5}x=\frac{1}{5}\)
\(\implies x^2 - \frac{7}{5}x + \frac{49}{100} =\frac{1}{5}+\frac{49}{100}\)
\(\implies (x-\frac{7}{10})^2=\frac{20+49}{100}\)
\(\implies (x-\frac{7}{10})^2=\frac{69}{100}\)
\(\implies (x-\frac{7}{10}) = \pm\sqrt{\frac{69}{100}}\)
\(\implies x=\frac{7}{10} \pm\sqrt{\frac{69}{100}}\)
Thus,
\(x=\frac{7}{10}+\sqrt{\frac{69}{100}}=1.53066238629\approx 1.53\)
or
\(x=\frac{7}{10}-\sqrt{\frac{69}{100}}=-0.13066238629\approx -0.13\)
Thus, the solution of the given equation are x ≈ 1.53 and x ≈ -0.13.
