Question

which of the following are solutions to the quadratic equation check all that apply x ^ 2 + 10x + 25 = 2

Answer 1

to solve the equation you first need to bring it to factors and by doing that you first need to let the equation equal 0 hence you need to minus 2 on both sides of the equation therefore

x^2 + 10x + 25 - 2 =2 - 2

therefore

x^2 + 10x +23 = 0

now since the equation cannot be factored, we use the formula.

x=
`\frac{-b +- \sqrt{b^(2)-4ac } }{2a}`

where

a=1

b=10

c=23

note we use the coefficients only.

therefore x =
`\frac{-10 -+ \sqrt{10^(2)-4(1)(23) } }{2(1)}`

=
`(-10-+√(100-92) )/(2)`

=
`(-10-+√(8) )/(2)`

then we form two equations according to negative and positive symbols

x=
`(-10+√(8) )/(2) or x =(-10-√(8) )/(2)`

therefore x =
`-5+√(2)` or x=
`-5-√(2)`