Solve the problem.
-The formula $N = 2 x ^ { 2 } + 6 x + 3$ represents the number of households $N$, in thousands, in a certain city that have a computer x years after 1990 . According to the formula, in what year were there 111 thousand households with computers in this city?
A) 1995
B) 1994
C) 1996
D) 1997

Question

Quizplus · Accepted Answer

To find the year when there were 111 thousand households with computers, we substitute $N = 111$ into the given formula and solve for $x$:$$111 = 2x^2 + 6x + 3$$Subtract 111 from both sides to set the equation to 0:$$0 = 2x^2 + 6x - 108$$Divide the entire equation by 2 to simplify:$$0 = x^2 + 3x - 54$$Factoring the quadratic equation:$$(x + 9)(x - 6) = 0$$This gives us two possible values for $x$: $x = -9$ or $x = 6$. Since $x$ represents years after 1990 and cannot be negative, we take $x = 6$.Therefore, the year was $1990 + 6 = 1996$.

Solve the Problem N=2x2+6x+3N = 2 x ^ { 2 } + 6 x + 3N=2x2+6x+3

Solve the Problem $N = 2 x ^ { 2 } + 6 x + 3$