Question

(x+2)^2-(x-3)^2= 3,2x^2

Answer 1

$(x + 2)^2-(x-3)^2=3,\!2x^2\\\\x^2+2x\cdot2+2^2-(x^2-2x\cdot3+3^2)=3,\!2x^2\\\\x^2+4x+4-x^2+6x-9=3,\!2x^2\\\\x^2+4x+4-x^2+6x-9-3,\!2x^2=0\\\\-3,\!2x^2+(4+6)\cdot x+(4-9)=0\\\\-3,\!2x^2+10x-5=0\;|\cdot(-1)\\\\3,\!2x-10x+5=0\\\\D=b^2-4ac=(-10)^2-4\cdot3,\!2\cdot5=100-64=36\\\\\\x_{1,2}=\dfrac{-b\pm\sqrt{D}}{2a}=\dfrac{-(-10)\pm\sqrt{36}}{2\cdot3,\!2}=\dfrac{10\pm6}{6,\!4}\\\\\\x_1=\dfrac{10-6}{6,\!4}=\dfrac{4}{6,\!4}=0,\!625\\\\\\x_2=\dfrac{10+6}{6,\!4}=\dfrac{16}{6,\!4}=2,\!5\\\\\\x_1=0,\!625\;,\;x_2=2,\!5$