Solve the equation below by completing the square. If the solution is not a real number state no real solution x^2+2x=63
To solve the given equation x^2 + 2x = 63 by completing the square, we first need to rearrange the terms:
x^2 + 2x - 63 = 0
Next, we need to complete the square. To do this, take half of the coefficient of x (which is 2) and square it:
(2/2)^2 = 1
Now, add and subtract this value inside the parenthesis:
x^2 + 2x + 1 - 1 = 63
(x + 1)^2 - 1 = 63
Now, bring the constant term to the other side of the equation:
(x + 1)^2 = 64
Next, take the square root of both sides of the equation:
x + 1 = ±√64
x + 1 = ±8
x = -1 ± 8
Therefore, the solutions to the equation x^2 + 2x = 63 are x = -1 + 8 = 7 and x = -1 - 8 = -9.