To solve the equation x^2 + 9x - 14 = 0 by completing the square, we first need to move the constant term to the other side:
x^2 + 9x = 14
Next, we need to find the value that completes the square. This value is calculated by taking half of the coefficient of x (which is 9 in this case) and squaring it:
(9/2)^2 = 81/4
Now we add and subtract this value inside the parentheses:
x^2 + 9x + 81/4 = 14 + 81/4
x^2 + 9x + 81/4 = 56/4 + 81/4
x^2 + 9x + 81/4 = 137/4
The left side of the equation can now be written as a square:
(x + 9/2)^2 = 137/4
Taking the square root of both sides gives:
x + 9/2 = ±√(137/4)
x + 9/2 = ±√137 / 2
x = -9/2 ± √137 / 2
Therefore, the solutions are x = -9/2 + √137 / 2, x = -9/2 - √137 / 2, which in decimal form are approximately:
10.35, -1.35
Solve the equation by completing the square.
x squared plus 9 x minus 14 equals 0
(1 point)
Responses
10.35, 1.35
10.35, 1.35
10.35, negative 1 point 35
10.35, Image with alt text: negative 1 point 35
negative 10.35, negative 1.35
Image with alt text: negative 10.35, negative 1.35
negative 10.35, 1.35
Image with alt text: negative 10.35 , 1.35
1 answer
1 answer