Question

completing the square of 4x (3x+2)= x+12

Answer 1

4x (3x+2)= x+12
12x^2+8x=x+12
12x^2+8x-x-12=0
12x^2+7x-12=0
12x+16-9x-12=0
4x(3x+4)-3(3x+4)=0
(4x-3)(3x+4) = 0
x = 3/4 or x = -4/3

Answer 2

Welcome to OpenStudy @Uly

Answer 3

I wouldn't call that completing the square, although it does get the right answer.

\[4x(3x+2) = x+12\]\[12x^2+8x = x + 12\]\[12x^2+7x = 12\]Divide through by 12 to get leading coefficient of 1 for completing the square
\[x^2+\frac{7}{12}x = 1\]Take half of the coefficient of \(x\), square, and add to both sides to complete the square
\[x^2 + \frac{7}{12}x + (\frac{7}{24})^2 = 1 + (\frac{7}{24})^2\]Rewrite LHS as perfect square\[\frac{1}{24^2}(24x+7)^2 = \frac{625}{576}\]Cancel common factor
\[(24x+7)^2 = 625\]Take square root of both sides\[24x+7 = \pm 25\]Solve for \(x\)\[24x = -7\pm25\]\[x = \frac{3}{4}, ~x = -\frac{4}{3}\]

Answer 4

yeahh..totally..the first one is not a completing the square.