Solve the equation by completing the square x + 9x - 14 = 0

Answer 1

To solve the equation x + 9x - 14 = 0 by completing the square, we first need to group the x terms together:

x^2 + 9x = 14

Next, we need to complete the square by taking half of the coefficient of the x term, squaring it, and adding it to both sides of the equation:

x^2 + 9x + (9/2)^2 = 14 + (9/2)^2
x^2 + 9x + 81/4 = 14 + 81/4
(x + 9/2)^2 = 14 + 81/4
(x + 9/2)^2 = 56/4 + 81/4
(x + 9/2)^2 = 137/4

Now, we can take the square root of both sides to solve for x:

x + 9/2 = ±√(137/4)
x + 9/2 = ±√137 / 2
x = -9/2 ± √137 / 2

Therefore, the solutions to the equation x + 9x - 14 = 0 are:

x = (-9 + √137) / 2 and x = (-9 - √137) / 2.