Question

solve this quadratic equation by completing the square. x2+2x=20

x=1 plus or minus square root of 24
x=-1 plus or minus square root of 24
x=-1 plus or minus square root of 21
x=1 plus or minus square root of 21

Answer 1

1. \[x^2 + 2x = 20 \rightarrow x^2 + 2x - 20 = 20 - 20\]
2. \[ x^2 + 2x - 20 =0 \rightarrow x^2 + 2x - 20 + 20 = 0 + 20\]
3. \[x^2 + 2x = 20 \rightarrow x^2 + 2x + (2 \div 1) = 20 + (2 \div 1)\]
4. \[x^2 + 2x + 1 = 20 + 1 \rightarrow \sqrt{(x + 1)^2} = \sqrt{21} \rightarrow (x+1) \pm \sqrt{21}\]

Answer 2

which "completes" the square?

Hint: only one later takes square root of a perfect square

Answer 3

so is it x= -1 plus or minus square root of 21?

Answer 4

should be x+1 = \(\pm \sqrt{21}\)
solve for x