Question

Solve for x in the equation x squared + 2 x + 1 = 17.

Answer 1

Answer:

Option B.

Step-by-step explanation:

The given equation is

$x^2+2x+1=17$

Subtract both sides by 17.

$x^2+2x+1-17=17-17$

$x^2+2x-16=0$          .... (1)

If a quadratic equation is $ax^2+bx+c=0$, then by quadratic formula

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

In equation (1), a=1, b=2 and c=-16. Using quadratic formula we get

$x=\dfrac{-(2)\pm \sqrt{(2)^2-4(1)(-16)}}{2(1)}$

$x=\dfrac{-2\pm \sqrt{4+64}}{2}$

$x=\dfrac{-2\pm \sqrt{68}}{2}$

$x=\dfrac{-2\pm 2\sqrt{17}}{2}$

Taking out common factors.

$x=\dfrac{2(-1\pm \sqrt{17})}{2}$

$x=-1\pm \sqrt{17}$

Therefore, the correct option is B.

Answer 2

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

                                 $\sqrt{(x+1)^{2} } = \sqrt{17}$

                                 (x + 1) = $\sqrt{17}$

Result

                                x₁ = - 1 + $\sqrt{17}$

                                 x₂ = -1  - $\sqrt{17}$