Question

solve for x in the equation 3x² - 18x + 5 = 47.
○ x = 3 ± √23
○ x = 3 ± √51
○ x = 3 ± √41
○ x = 3 ± √5

Explanation:

Step1: Rearrange to standard form

Subtract 47 from both sides:
$3x^2 - 18x + 5 - 47 = 0$
$3x^2 - 18x - 42 = 0$
Divide all terms by 3:
$x^2 - 6x - 14 = 0$

Step2: Apply quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Here, $a=1$, $b=-6$, $c=-14$
Calculate discriminant:
$\Delta = (-6)^2 - 4(1)(-14) = 36 + 56 = 92$

Step3: Simplify the solution

$x = \frac{6 \pm \sqrt{92}}{2}$
Simplify $\sqrt{92} = \sqrt{4 \times 23} = 2\sqrt{23}$
$x = \frac{6 \pm 2\sqrt{23}}{2} = 3 \pm \sqrt{23}$

Answer:

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