Question

Solve the quadratic equation by completing the square. 6x2 + 4x - 5 = 0

Answer 1

`$x_(1)=-(2+√(34))/(6)$`

`$x_(2)=-(2-√(34))/(6)$`

Explanation:

Quadratic Equation given:

`6x^2 + 4x - 5 = 0`

Start dividing both sides by 6.

`$(6)/(6) x^2 +(4)/(6) x - (5)/(6) = (0)/(6) $`

`$x^2 +(2)/(3) x - (5)/(6) = 0 $`

`$x^2 +(2)/(3) x = (5)/(6) $`

Once,
`$\left( (2)/(3) \cdot (1)/(2) \right)^2=(1)/(9) $`

`$x^2 +(2)/(3) x+(1)/(9) = (5)/(6)+(1)/(9) $`

`$\left(x+(1)/(3) \right)^2 = (17)/(18)} $`

`$x+(1)/(3) =\pm\sqrt{(17)/(18)} } $`

Solving
`$\sqrt{(17)/(18)} $`

`$\sqrt{(17(18))/(18(18))}= \sqrt{(306)/(324)}=(3√(34) )/(18) =(√(34) )/(6) $`

Then,

`$x+(1)/(3) =\pm(√(34) )/(6) $`

`$x =-(1)/(3) \pm(√(34) )/(6) $`

`$x_(1)=-(2+√(34))/(6)$`

`$x_(2)=-(2-√(34))/(6)$`