Question

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

Answer 1

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

`m=((2x+k)^2-(12x+9))/(x^2)`

Step-by-step 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 \\ (\mleft(2x+k\mright)^2-\mleft(12x+9\mright))/(x^2)=(mx^2)/(x^2) \\ m=((2x+k)^2-(12x+9))/(x^2) \end{gathered}`