Solve the problem.
-The formula $$N = 4 x ^ { 2 } + 3 x + 2$$ 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 164 thousand households with
Computers in this city?
A)1995
B)1996
C)1997
D)1994

Question

Quizplus · Accepted Answer

To find the year when there were 164 thousand households with computers, we substitute $N = 164$ into the given formula and solve for $x$:$$164 = 4x^2 + 3x + 2$$First, move all terms to one side to set the equation to 0:$$4x^2 + 3x + 2 - 164 = 0$$$$4x^2 + 3x - 162 = 0$$Next, we solve this quadratic equation for $x$. This can be done by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula where $a = 4$, $b = 3$, and $c = -162$:$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$$$x = \frac{-3 \pm \sqrt{3^2 - 4(4)(-162)}}{2(4)}$$$$x = \frac{-3 \pm \sqrt{9 + 2592}}{8}$$$$x = \frac{-3 \pm \sqrt{2601}}{8}$$$$x = \frac{-3 \pm 51}{8}$$The positive solution that makes sense in this context is:$$x = \frac{48}{8} = 6$$Since $x$ represents the number of years after 1990, we add 6 to 1990 to find the year:$$1990 + 6 = 1996$$Therefore, there were 164 thousand households with computers in the city in 1996.

Solve the Problem N=4x2+3x+2N = 4 x ^ { 2 } + 3 x + 2N=4x2+3x+2

Solve the Problem $N = 4 x ^ { 2 } + 3 x + 2$