Solve -16t^2-8t=10 by completing the square
To solve the quadratic equation -16t^2 - 8t = 10 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
-16t^2 - 8t - 10 = 0
Step 2: Divide the entire equation by the coefficient of the squared term to make the coefficient equal to 1:
16t^2 + 8t + 10 = 0
Step 3: Divide every term by the leading coefficient (which is 16) to simplify the equation further:
t^2 + (8/16)t + (10/16) = 0
t^2 + (1/2)t + 5/8 = 0
Step 4: Take the coefficient of the t-term (in this case, 1/2), divide it by 2, square it, and add it to both sides of the equation:
t^2 + (1/2)t + (1/2*2)^2 = -5/8 + (1/2*2)^2
Simplifying the expression:
t^2 + (1/2)t + (1/4) = -5/8 + 1/4
t^2 + (1/2)t + (1/4) = -5/8 + 2/8
t^2 + (1/2)t + (1/4) = -3/8
Step 5: Factor the left side of the equation:
(t + 1/4)^2 = -3/8
Step 6: To complete the square, take the square root of both sides of the equation:
t + 1/4 = ±√(-3/8)
Step 7: Solve for t:
t = -1/4 ± √(-3/8)
Since the square root of a negative number cannot be expressed in terms of real numbers, t will have no real solutions in this case. However, it does have complex solutions.