Question

Solve x2 + 1/2x +1/16=4/9

Answer 1

x = 0.417 or x = -0.917

Explanation:

We are given the following expression and we are to solve it for the variable x:

`x ^2 + \frac { 1 } { 2 } x + \frac { 1 } { 1 6 } = \frac { 4 } { 9 }`

We will find the least common multiple of 2. 6 and 9:

`x^2 * 144 +(1)/(2)x * 144 +(1)/(16) * 144 = (4)/(9) * 144`

Simplifying it to get:

`144x^2+72x+9=64`

`144x^2+72x+9-64=0`

`144x^2+72x-55=0`

Using the quadratic formula to solve for x:

`x=(-b \pm√(b^2-4ac) )/(2a)`

`x=(-72 \pm√(72^2-4(144)(-55)) )/(2a)`

`x=(5)/(12)` or
`0.417`

`x=-(11)/(12)` or
`-0.917`