Solve the equation for all values of x by completing the square.
x, squared, plus, 2, x, equals, 35
x
2
+2x=
35
To solve the equation x^2 + 2x = 35 by completing the square, we first move the constant term to the other side to set the equation equal to 0:
x^2 + 2x - 35 = 0
Next, we need to complete the square by adding and subtracting (b/2)^2 to the equation, where b is the coefficient of x (in this case, b = 2):
x^2 + 2x + (2/2)^2 = 35 + (2/2)^2
x^2 + 2x + 1 = 35 + 1
x^2 + 2x + 1 = 36
Now we can rewrite the left side of the equation as a perfect square:
(x + 1)^2 = 36
Take the square root of both sides to solve for x:
x + 1 = ±6
x = -1 ± 6
x = -7 or x = 5
Therefore, the solutions are x = -7 and x = 5.