Question

Solve the quadratic equation by completing the square.

x^+12x+30=0

First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.

Form:
( x + _ )^2 = _
or
( x - _ )^2 = _

Solution:
x = _

^ Please use the template above to answer ^

Answer 1

`x^(2) +12x+30=0`

we first complete the square, by writing 12 as 2*6, then adding and subtracting
`6^(2) =36`


`(x^(2) +12x+36)-36+30=0`


`(x+6)^(2) -36+30=0`


`(x+6)^(2) -6=0`


`(x+6)^(2) =6`

Solution:

take the square root of both sides


`\sqrt{(x+6)^(2) } = √(6)`


`|(x+6)|= √(6)` because
`\sqrt{ A^(2) }=|A|`

then

i)
`x+6= √(6)`, so
`x= -6+√(6)`
ii)
`x+6= -√(6)` so
`x= -6-√(6)`

Solution: x∈{
`x= -6+√(6)`,
`x= -6-√(6)`}