Solve for x in the equation x2+2x+1=17

If you meant 2x + 2x + 1 = 17: x = 4
Solve for x by simplifying both sides of the equation, then isolating the variable. 

If you meant x2 + 2x + 1 = 17: x ≈ 3.1231056,−5.1231056x
Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula. x = −1 ± √17x

Simplifying
 x2 + 2x + 1 = 17
 Reorder the terms
1 + 2x + x2 = 17
 Solving
1 + 2x + x2 = 17
 Solving for variable 'x'.
Reorder the terms:
1 + -17 + 2x + x2 = 17 + -17
  Combine like terms:
 1 + -17 = -16 -16 + 2x + x2 = 17 + -17 C
ombine like terms:
 17 + -17 = 0 -16 + 2x + x2 = 0
  Begin completing the square.
 Move the constant term to the right:
  Add '16' to each side of the equation
. -16 + 2x + 16 + x2 = 0 + 16
 Reorder the terms:
 -16 + 16 + 2x + x2 = 0 + 16
 Combine like terms:
 -16 + 16 = 0 0 + 2x + x2 = 0 + 16 2x + x2 = 0 + 16
 Combine like terms:
 0 + 16 = 16 2x + x2 = 16
  The x term is 2x. Take half its coefficient (1).
Square it (1) and add it to both sides. Add '1' to each side of the equation.
2x + 1 + x2 = 16 + 1
  Reorder the terms:
 1 + 2x + x2 = 16 + 1
 Combine like terms:
 16 + 1 = 17 1 + 2x + x2 = 17
  Factor a perfect square on the left side:
 (x + 1)(x + 1) = 17
  Calculate the square root of the right side:
 4.123105626
 Break this problem into two subproblems by setting
  (x + 1) equal to 4.123105626 and -4.123105626. x + 1 = 4.123105626
 Simplifying
x + 1 = 4.123105626
 Reorder the terms:
1 + x = 4.123105626
  Solving
 1 + x = 4.123105626
  Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation.
1 + -1 + x = 4.123105626 + -1
  Combine like terms:
 1 + -1 = 0 0 + x = 4.123105626 + -1 x = 4.123105626 + -1
  Combine like terms:
 4.123105626 + -1 = 3.123105626 x = 3.123105626
  Simplifying
 x = 3.123105626
x + 1 = -4.123105626
 Simplifying
x + 1 = -4.123105626
 Reorder the terms:
1 + x = -4.123105626
 Solving
 1 + x = -4.123105626
 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation.
 1 + -1 + x = -4.123105626 + -1
  Combine like terms:
 1 + -1 = 0 0 + x = -4.123105626 + -1 x = -4.123105626 + -1
  Combine like terms:
 -4.123105626 + -1 = -5.123105626 x = -5.123105626
 Simplifying x = -5.123105626
x = {3.123105626, -5.123105626}