Solve for x in the equation 3 x squared minus 18 x + 5 = 47.
A) x = 3 plus-or-minus StartRoot 23 EndRoot
B) x = 3 plus-or-minus StartRoot 51 EndRoot
C) x = 3 plus-or-minus StartRoot 41 EndRoot
D) x = 3 plus-or-minus StartRoot 5 EndRoot
To solve the quadratic equation [tex]3x^2-18x+5=47[/tex], we have to express it like [tex]ax^2+bx+c=0[/tex], where "a" is the coefficient that accompanies the squared term, "b" is the coefficient that accompanies the linear term, and "c" is the constant. In this case, the equation can be written as: [tex]3x^2-18x+5-47=0[/tex]⇒[tex]3^2-18x-42=0[/tex].
Then, we just have to apply the well known quadratic formula [tex]\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex] to find the roots of x. Given the values of the coefficients, we can find the solution by calculating [tex]\frac{18(+-)\sqrt{(-18)^2-4\times3\times(-42)} }{2\times3}=\frac{18(+-)\sqrt{324+504} }{6}=\frac{18(+-)\sqrt{828} }{6}[/tex]. (We just replace the values of our equation in the formula, and then simplify step by step).
This will result in [tex]x= 3(+-) 4.7958[/tex]. Because [tex]4.7958^2=23[/tex], we just can express the solution as [tex]x=3(+-)\sqrt{23}[/tex], which is option A.
