Question

Solve for x in the equation 3x2-18x+5=47

Answer 1

ANSWER

$x = 3 \pm \: \sqrt{23}$


EXPLANATION

The given equation is

$3 {x}^{2} - 18x + 5 = 47$

We rewrite in standard quadratic form to obtain,
$3 {x}^{2} - 18x + 5 - 47 = 0$


$3 {x}^{2} - 18x - 42 = 0$



Dividing through by 3, we obtain,


${x}^{2} - 6x - 14= 0$



We have

$a=1,b=-6,c=-14$

The solution is given by the formula,

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$


We substitute the values to obtain,


$x = \frac{ - - 6 \pm \sqrt{ {( - 6)}^{2} - 4(1)( - 14)} }{2(1)}$



$x = \frac{ 6 \pm \sqrt{ 36 +56} }{2}$


$x = \frac{ 6 \pm \sqrt{ 92} }{2}$


$x = \frac{ 6 \pm 2\sqrt{ 23} }{2}$



$x = 3 \pm \: \sqrt{23}$

The correct answer is A.

Answer 2

Answer:

Choice A is correct answer.

Step-by-step explanation:

We have given a quadratic equation.

3x²-18x+5 = 47

3x²-18x+5-47 = 0

3x²-18x-42 = 0

ax²+bx+c = 0 is general quadratic equation.

Comparing above equations, we have

a  =  3 , b =  -18 and c  =  -42

x = (-b±√b²-4ac) / 2a is quadratic formula to solve equation.

Putting given values in above formula, we have

x = (-(-18)±√(-18)²-4(3)(-42) ) / 2(3)

x = (18±√324+504) / 6

x = (18±√828) / 6

x = (18±√23×36) /6

x = (18±6√23) / 6

x = 6(3±√23) / 6

x = 3±√23 is solution of given equation.