Question

can you please help me solve this quadratic equation for x by factoring- 2x^2+(2x+4)^2=(2x+6)^2

Answer 1

x^2+(2x+4)^2=(2x+6)^2

Answer 2

first do FOIL for the (2x + 2)^2 and (2x + 6)^2

Answer 3

Then combine like terms and form one single quadratic equation and then factor

Answer 4

\[x ^{2} + (2x + 4)^{2} = (2x + 6)^{2}\]
\[x^{2} + (2x + 4) (2x + 4) = (2x + 6) (2x + 6)\]
\[x ^{2} + 4x ^{2} + 8x + 8x + 16 = 4x ^{2} + 12x + 12x + 36\]
\[x ^{2} = 4x + 4x + 20\]
\[x ^{2} - 8x - 20 = 0\]
\[(x - 10) (x + 2) = 0\]
\[x = 10 ; x = -2\]