solve by completeing the square
m^2-9/2m=3/2
m^2 -9/2m = 3/2.
m^2 -9/2m + (9/4)^2 = 3/2 + (9/4)^2
m^2 - 9/2m +(9/4)^2 = 24/16 + 81/16
m^2 -9/2m + (9/4)^2 = 105/16
(m - 9/4)^2 = 105/16
Take sqrt of both sides:
m - 9/4 = (sqrt105)/4
m = 9/4 + (sqrt105)/4 = (9 +- sqrt105)/4
m = 4.8, and -0.31.
To solve the equation by completing the square, follow these steps:
1. Move the constant term to the other side of the equation, so the equation becomes m^2 - (9/2)m = 3/2.
2. Take half of the coefficient of the m term (-9/2) and square it: (-9/2)/2 = (-9/4)^2 = 81/16.
3. Add the square obtained in step 2 to both sides of the equation: m^2 - (9/2)m + 81/16 = 3/2 + 81/16.
4. Simplify the right side of the equation: 3/2 + 81/16 = 24/16 + 81/16 = 105/16.
5. Rewrite the left side as a perfect square: (m - 9/4)^2 = 105/16.
6. Take the square root of both sides of the equation, considering both positive and negative roots: m - 9/4 = ±√(105/16).
7. Solve for m:
- m - 9/4 = √(105/16):
m = √(105/16) + 9/4.
- m - 9/4 = -√(105/16):
m = -√(105/16) + 9/4.
So, the solutions to the equation m^2 - (9/2)m = 3/2 by completing the square are:
- m = √(105/16) + 9/4
- m = -√(105/16) + 9/4