Question

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

No real solutions
x ≈ −0.65 and x ≈ 7.65
x ≈ −1.53 and x ≈ 0.13
x ≈ −0.13 and x ≈ 1.53

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

Explanation:

Here, the given equation is,

`5x^2-7x=1`

`\implies x^2 - (7)/(5)x=(1)/(5)`

`\implies x^2 - (7)/(5)x + (49)/(100) =(1)/(5)+(49)/(100)`

`\implies (x-(7)/(10))^2=(20+49)/(100)`

`\implies (x-(7)/(10))^2=(69)/(100)`

`\implies (x-(7)/(10)) = \pm\sqrt{(69)/(100)}`

`\implies x=(7)/(10) \pm\sqrt{(69)/(100)}`

Thus,

`x=(7)/(10)+\sqrt{(69)/(100)}=1.53066238629\approx 1.53`

or

`x=(7)/(10)-\sqrt{(69)/(100)}=-0.13066238629\approx -0.13`

Thus, the solution of the given equation are x ≈ 1.53 and x ≈ -0.13.