Question

Which of the following are solutions to the equation below? Check all that apply. x2 + 10x + 25 = 2

Answer 1

-5+√2 and -5-√2

Explanation:

With the quadratic formula:

`\displaystyle x^2 + 10x + 25 = 2\\\\x^2+10x+23=0\\\\x=(-10\pm√(10^2-4(1)(23)))/(2(1))=(-10\pm√(100-92))/(2)=(-10\pm√(8))/(2)=(-10\pm2√(2))/(2)=-5\pm√(2)`

We can also complete the square (which is faster):

`x^2+10x+25=2\\(x+5)^2=2\\x+5=\pm√(2)\\x=-5\pm√(2)`