h^2+3h-1=0 Solve by completing the square. How do I do this?
h^2 + 3 h = 1
take half of 3, square it, add to both sides
h^2 + 3 h + (3/2)^2 = 1 + 9/4 = 13/4
(h+3/2)^2 = 13/4
h + 3/2 = +/-(1/2)sqrt (13)
h = -1.5 +/- .5 sqrt(13)
To solve the equation using the method of completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
h^2 + 3h = 1
Step 2: Make sure the coefficient of the squared term (h^2) is 1. If it's not already, divide the whole equation by that coefficient. In this case, the coefficient is already 1, so we can skip this step.
Step 3: Take half of the coefficient of the linear term (3 in this case) and square it. Add this result to both sides of the equation. It completes the square on the left side of the equation. The equation becomes:
h^2 + 3h + (3/2)^2 = 1 + (3/2)^2
Simplifying gives:
h^2 + 3h + 9/4 = 1 + 9/4
Step 4: The left side of the equation can now be written as a perfect square. Factor it:
(h + 3/2)^2 = 13/4
Step 5: Take the square root of both sides of the equation:
h + 3/2 = ±√(13/4)
Step 6: Solve for h by subtracting 3/2 from both sides of the equation:
h = -3/2 ± √(13/4)
Therefore, the solution to the equation h^2 + 3h - 1 = 0, using the method of completing the square, is h = -3/2 ± √(13/4)