Question

(2x+K)^2=(mx^2+12x+9)Solve for K Solve for m

Answer 1

$k=(\sqrt[]{mx^2+12x+9})-2x$

$m=\frac{(2x+k)^2-(12x+9)}{x^2}$

Explanation

$(2x+k)^2=mx^2+12x+9$

Step 1

obtain the square root in both sides

$\begin{gathered} (2x+k)^2=mx^2+12x+9 \\ \sqrt[]{\mleft(2x+k\mright)^2}=\sqrt[]{mx^2+12x+9} \\ 2x+k=\sqrt[]{mx^2+12x+9} \end{gathered}$

Step 2

subtract 2x in both sides

$\begin{gathered} 2x+k=\sqrt[]{mx^2+12x+9} \\ 2x+k-2x=(\sqrt[]{mx^2+12x+9})-2x \\ k=(\sqrt[]{mx^2+12x+9})-2x \\ \end{gathered}$

Step 3

solve for m

$(2x+k)^2=mx^2+12x+9$

a) subtract (12x+9) in both sides

$\begin{gathered} (2x+k)^2=mx^2+12x+9 \\ (2x+k)^2-(12x+9)=mx^2+12x+9-(12x+9) \\ (2x+k)^2-(12x+9)=mx^2 \end{gathered}$

b) divide each side by square x

$\begin{gathered} \mleft(2x+k\mright)^2-\mleft(12x+9\mright)=mx^2 \\ \frac{\mleft(2x+k\mright)^2-\mleft(12x+9\mright)}{x^2}=\frac{mx^2}{x^2} \\ m=\frac{(2x+k)^2-(12x+9)}{x^2} \end{gathered}$