Question

Solve.

x² + 4x + 4 = 18


​ A x=−4±3√ ​2

​ B x=2±3√ ​2

​ C x=4±9√ ​2

D x=−2±3√2

Answer 1

Solve.

x² + 4x + 4 = 18


​ A x=−4±3√ ​2

​ B x=2±3√ ​2

​ C x=4±9√ ​2

D x=−2±3√2




`x^2 + 4x + 4 = 18 \\ \\ x^2+4x+4-18= 0 \\ \\ x^2+4x-14=0 \\ \\ x_1_y_2= (-b\pm √(b^2-4ac) )/(2a) \qquad a= 1\qquad b= 4\qquad c= -14 \\ \\ \\ x_1_y_2= (-4\pm √(4^2-4(1)(-14)) )/(2(1)) \\ \\ \\ x_1_y_2= (-4\pm √(16-(-56)) )/(2) \\ \\ \\ x_1_y_2= (-4\pm √(72) )/(2) \\ \\ \\ x_1= (-4+ √(72) )/(2) \qquad\qquad x_2= (-4+ √(72) )/(2)\\ \\ \\ x_1= (-4+ √(2^3*3^2) )/(2) \qquad\qquad x_2= (-4- √(2^3*3^2) )/(2)`


`x_1= (-4+2*3 √(2) )/(2) \qquad\qquad x_2= (-4- 2*3√(2) )/(2) \\ \\ \\ x_1= (-4+6 √(2) )/(2) \qquad\qquad x_2= (-4- 6√(2) )/(2) \\ \\ \\ x_1= (-4)/(2) + (6 √(2) )/(2) \qquad\qquad x_2= (-4)/(2)- ( 6√(2) )/(2) \\ \\ \\ x_1= -2 + 3 √(2) \qquad\qquad\quad x_2= -2- 3√(2) \\ \\ \\ \boxed{x= -2\pm 3√(2) } \to D)`

Answer 2

This was the correct answer, I even provided proof from my own test. Hope this helps!