Question

3x squared -42x+9=-5 for completing the square

Answer 1

$3x^2 -42x + 9 = -5$

Subtract 9 from both sides
$3x^2 -42x = -5 - 9$

$3x^2 -42x = -14$

Divide by 3 through
$x^2 -14x = - \dfrac{14}{3}$

Add (b/2)^2 to form perfect square
$x^2 -14x + (\dfrac{14}{2})^2 = - \dfrac{14}{3} + (\dfrac{14}{2})^2$

Form perfect square
$(x -7)^2 = \dfrac{7}{3}$

square root both sides
$(x -7) = \pm \sqrt{\dfrac{7}{3}}$

Add 7 to both sides
$x = \pm \sqrt{\dfrac{7}{3}} + 7$

Rewrite the answer into 2 different answers
$x = 7 + \sqrt{\dfrac{7}{3}} \ or \ 7 - \sqrt{\dfrac{7}{3}}$



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