To solve the equation by completing the square, we need to rewrite the equation in the form (x + p)^2 = q, where p and q are constants.
To begin, let's move the constant term (-14) to the right side of the equation:
x^2 + 9x = 14
Next, we need to calculate half of the coefficient of x, square it, and add it to both sides of the equation:
9/2 = 4.5
(9/2)^2 = 20.25
x^2 + 9x + 20.25 = 14 + 20.25
x^2 + 9x + 20.25 = 34.25
Now, we can rewrite the left side of the equation as the square of a binomial:
(x + 4.5)^2 = 34.25
Taking the square root of both sides of the equation, we get:
x + 4.5 = ±√(34.25)
To solve for x, we subtract 4.5 from both sides of the equation:
x = -4.5 ±√(34.25)
Therefore, the solutions to the equation x^2 + 9x - 14 = 0, solved by completing the square, are:
x = -4.5 + √(34.25) or x = -4.5 - √(34.25)
Solve the equation by completing the square.
x^2+9x-14=0
1 answer