Question

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

Answer 1

Choice A is correct answer.

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.

Answer 2

ANSWER


`x = 3 \pm \: √(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 = ( 6 \pm √( 36 +56) )/(2)`



`x = ( 6 \pm √( 92) )/(2)`



`x = ( 6 \pm 2√( 23) )/(2)`




`x = 3 \pm \: √(23)`

The correct answer is A.