Question

How do you solve `c^2 + 8c + 2 = 5c + 15` by completing the square?

Answer 1

See the Explanation:

Explanation:

`c^2 + 8c + 2 = 5c + 15`
`c^2 + 3c = 13`
`c^2 + 2(3/2)c = 13`
`c^2 + 2(3/2)c + (3/2)^2 - (3/2)^2 = 13`
`(c + 3/2)^2 - (3/2)^2 = 13`
`(c + 3/2)^2 = 13 + 9/4`
`c + 3/2 = +- sqrt(13 + 9/4)`
`c = -3/2 +- sqrt61/2`

Answer 2

`c=-3/2+-1/2sqrt61`

Explanation:

`"rearrange equation into "color(blue)"standard form"`

`"subtract "5c+15" from both sides"`

`rArrc^2+3c-13=0larrcolor(blue)"in standard form"`

`"using the method of "color(blue)"completing the square"`

`• " the coefficient of the "c^2" term must be 1 which it is"`

`• " add/subtract "(1/2"coefficient of the c-term")^2" to"`
`c^2+3c`

`c^2+2(3/2)c color(red)(+9/4)color(red)(-9/4)-13=0`

`rArr(c+3/2)^2-61/4=0`

`rArr(c+3/2)^2=61/4`

`color(blue)"take the square root of both sides"`

`rArrc+3/2=+-sqrt(61/4)larrcolor(blue)"note plus or minus"`

`rArrc+3/2=+-1/2sqrt61`

`"subtract "3/2" from both sides"`

`rArrc=-3/2+-1/2sqrt61larrcolor(red)"exact solutions"`