Question

What are the approximate solutions of 2x2 + x = 14, rounded to the nearest hundredth? x ≈ −2.41 and x ≈ 2.91 x ≈ −2.91 and x ≈ 2.41 x ≈ −5.82 and x ≈ 4.82 no real solutions?

Answer 1

Answer: Hello mate!

We have the equation 2x^2 + x = 14

let's solve it for x:

2x^2 + x - 14 = 0

the solutions can be obtained with the equation:

`x = (-1 +/- √(1 - 4*2*(-14)) )/(2*2)  = (-1 +/- √(113) )/(4) =(-1 +/-10.63)/(4)`

then the solutions are:

(-1 - 10.63)/4 = -2.907, that rounded to the hundreths is equal to -2.91 (because the number after the hundredth place is a 7, so we round up)

and

(-1 +10.63)/4 = 2.407, that when rounded to the hundreths place is equal to 2.41 (the same reason as before)

then the answers are -2.91 and 2.41