Question

Solve by completing the square: 2s² + 5s = 3

Answer 1

To solve the equation 2s² + 5s = 3 by completing the square, follow these steps: Move the constant term to the right side of the equation, divide the equation by the coefficient of the squared term, take half of the coefficient of the linear term and square it, add the result to both sides, factor the left side as a perfect square, simplify, take the square root, and solve for s.

Step-by-step explanation:

To solve the equation 2s² + 5s = 3 by completing the square, follow these steps:

1. Move the constant term to the right side of the equation to make it equal to zero: 2s² + 5s - 3 = 0.
2. Divide the entire equation by the coefficient of the squared term to make it equal to 1: s² + (5/2)s - 3/2 = 0.
3. Take half of the coefficient of the linear term and square it: (5/4)² = 25/16.
4. Add the result from step 3 to both sides of the equation: s² + (5/2)s + 25/16 = 3/2 + 25/16.
5. Factor the left side of the equation as a perfect square: (s + 5/4)² = 3/2 + 25/16.
6. Simplify the right side of the equation: (s + 5/4)² = 49/8.
7. Take the square root of both sides of the equation: s + 5/4 = ±√(49/8).
8. Solve for s: s = -5/4 ± √(49/8).