Respuesta :

[tex]x = 3+- \sqrt{23} [/tex]
TaeKwonDoIsDead

Answer:

[tex]x[/tex]≅[tex]7.80,-1.80[/tex] (rounded to 2 decimal places)


Step-by-step explanation:

This is a quadratic equation : [tex]3x^2-18x+5=47[/tex]

Bringing everything to left side:

[tex]3x^2-18x+5=47\\3x^2-18x+5-47=0\\3x^2-18x-42=0[/tex]


We can use the quadratic formula to find the value(s) of x:

Quadratic Formula:

  • [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]

and

  • [tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

Where,

  • a is the coefficient of [tex]x^2[/tex]
  • b is the coefficient of [tex]x[/tex]
  • c is the constant term

For our question we have:

[tex]a=3\\b=-18\\c=-42[/tex]

Plugging in all the values we get:

[tex]x=\frac{-(-18)+\sqrt{(-18)^2-4(3)(-42)} }{2(3)}\\x=\frac{18+\sqrt{828} }{6}[/tex]

This is approximately 7.80

and

[tex]x=\frac{-(-18)-\sqrt{(-18)^2-4(3)(-42)} }{2(3)}\\x=\frac{18-\sqrt{828} }{6}[/tex]

This is approximately -1.80


So, [tex]x[/tex]≅[tex]7.80,-1.80[/tex]



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