Question

Solve for x in the equation x^2 + 2x + 1 = 17

Answer 1

Option(B) is the answer
Hope this helps you..!!

Answer 2

If you subtract 17 from both sides, the equation becomes

$x^2+2x-16 = 0$

and it's a quadratic equation in standard form, i.e. $ax^2+bx+c=0$

If you name the coefficients like this, the equation has solutions

$x_{1,2} = \cfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

So, if you plug your values for a,b and c you have

$x_{1,2} = \cfrac{-2\pm\sqrt{4-4\cdot 1 \cdot (-16)}}{2\cdot 1} = \cfrac{-2\pm\sqrt{68}}{2}$

Since 68 = 4 x 17, we have

$\sqrt{68} = \sqrt{4\times 17} = \sqrt{4}\sqrt{17} = 2\sqrt{17}$

So, the solutions can be written as

$\cfrac{-2\pm2\sqrt{17}}{2} = -1\pm \sqrt{17}$