Absolutely! Here's the entire solution process for the equation 5m² – 2m = 2 with the revised and simplified last steps:
1. Rearrange into Standard Quadratic Form:
- Subtract 2 from both sides: 5m² - 2m - 2 = 0
2. Use the Quadratic Formula:
- Identify the coefficients:
- a = 5
- b = -2
- c = -2
- Substitute into the quadratic formula: m = (-b ± √(b² - 4ac)) / 2a
- Simplify: m = (2 ± √(44)) / 10 m = (2 ± 2√11) / 10
3. Simplify and Find the Solutions:
- Factor out 2 from the numerator: m = 2(1 ± √11) / 10
- Cancel the common factor of 2: m = (1 ± √11) / 5
Therefore, the simplified solutions to the equation 5m² – 2m = 2 are:
- m₁ = (1 + √11) / 5
- m₂ = (1 - √11) / 5
