Question

"Solving Equations by Completing the Square: m^2+2m-48=-6

Answer 1

`m^2+2m-48=-6\\\\m^2+2m\cdot1+1^2-1^2=-6+48\\\\(m+1)^2-1=42\\\\(m+1)^2=42+1\\\\(m+1)^2=43\iff m+1=-√(43)\ \vee\ m+1=√(43)\\\\m=-1-√(43)\ \vee\ m=-1+√(43)`

Answer 2

`m^2+2m-48=-6 \\ \\ m^2+2m-48+6=0\\ \\m^2+2m-42=0\\ \\a=1, \ b= 2, \ c= -42 \\ \\\Delta = b^(2)-4ac = 2^(2)-4*1*(-42)= 4+168 =172 \\\\√(\Delta )=√(172) =√(4*43)=2√(43)\\ \\x_(1)=(-b-√(\Delta ))/(2a) =(-2-2√(43))/(2)=(2(-1-√(43)))/(2)= -1-√(43) \\ \\x_(2)=(-b+√(\Delta ))/(2a) = (-2+2√(43))/(2)=( 2(-1+√(43)))/(2)= -1+√(43)`