Question

Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q.

1 + 2x + 2x2 = 0

A) (x + 0.5)2 = 0.5


B) (x + 0.5)2 = -0.5


C) (x + 0.5)2 = 0.25


D) (x + 0.5)2 = -0.25

Answer 1

`\text{Use:}(*)\ (a+b)^2=a^2+2ab+b^2\\\\2x^2+2x+1=0\ \ \ \ |:2\\\\x^2+x+0.5=0\\\\x^2+2\cdot x\cdot0.5+0.5=0\\\\\underbrace{x^2+2\cdot x\cdot0.5+0.5^2}_((*))-0.5^2+0.5=0\\\\(x+0.5)^2-0.25+0.5=0\\\\(x+0.5)^2+0.25=0\ \ \ \ |-0.25\\\\(x+0.5)^2=-0.25\to D)`

Answer: D) (x + 0.5)2 = -0.25