Answer:
The answer to your question is the second option
Step-by-step explanation:
Process
1.- Write the equation
x² + 2x + 1 = 17
Factor the first term
(x + 1)² = 17
Get the square root
[tex]\sqrt{(x+1)^{2} } = \sqrt{17}[/tex]
(x + 1) = [tex]\sqrt{17}[/tex]
Result
x₁ = - 1 + [tex]\sqrt{17}[/tex]
x₂ = -1 - [tex]\sqrt{17}[/tex]
Answer:
Option B.
Step-by-step explanation:
The given equation is
[tex]x^2+2x+1=17[/tex]
Subtract both sides by 17.
[tex]x^2+2x+1-17=17-17[/tex]
[tex]x^2+2x-16=0[/tex] .... (1)
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then by quadratic formula
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
In equation (1), a=1, b=2 and c=-16. Using quadratic formula we get
[tex]x=\dfrac{-(2)\pm \sqrt{(2)^2-4(1)(-16)}}{2(1)}[/tex]
[tex]x=\dfrac{-2\pm \sqrt{4+64}}{2}[/tex]
[tex]x=\dfrac{-2\pm \sqrt{68}}{2}[/tex]
[tex]x=\dfrac{-2\pm 2\sqrt{17}}{2}[/tex]
Taking out common factors.
[tex]x=\dfrac{2(-1\pm \sqrt{17})}{2}[/tex]
[tex]x=-1\pm \sqrt{17}[/tex]
Therefore, the correct option is B.
