Question

Complete the Square:
5x^2+16x-40=8
(please show your steps)

Answer 1

Explanation:

divide through by the coefficient of
`x^(2)`

`(5x^(2) )/(5)` +
`(16x)/(5) + (-40)/(5) = (8)/(5)`

`x^(2) +(16)/(5)x -8 =(8)/(5)`

`x^(2) +(16)/(5) x = (8)/(5) +8`

`x^(2) + (16)/(5) x =(48)/(5)`

Add half of the square of the coefficient of x to both sides
`((1)/(2) X (16)/(5) ) ^(2)`

`x^(2) + (16)/(5)x + ((1)/(2) X (16)/(5) )^(2) =`
`(48)/(5) +((1)/(2) X (16)/(5) )^(2)`

`x^(2) +(16)/(5) x +((16)/(10)) ^(2) =(48)/(5) +(64)/(25)`

`(x +(16)/(10))^(2) =(304)/(25)`

`x +(16)/(10) =`±
`\sqrt{(304)/(25) }`

`x = -(16)/(10)` ±
`\sqrt{(304)/(25) }`

`x=-(16)/(10) + \sqrt{(304)/(25) }` or
`-(16)/(10) - \sqrt{(304)/(25) }`

`x = 1.89` or -5.09