Question

What are the approximate solutions of 5x2 − 7x = 1, rounded to the nearest hundredth?

Answer 1

5x^2 - 7x - 1 = 0 

x = (7 +/- sqrt(49 - (4)(5)(-1)))/10 
x = (7 +/- sqrt(69))/10 
x = -0.13, 1.53 

Answer 2

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.