1. x^2 − 10x − 12 = 0 2. x^2 − 10x = 12 3. x^2 − 10x + ? = 12 + ? 4. We factor and simplify to get:(x−5)2 = ? 5. At this point, we need to ? 6. After that is done, we will have: ? = ? 7. We get isolate the variable by: ? 8. Final answers are: ?
1. Given equation: x^2 − 10x − 12 = 0
2. Rewritten equation: x^2 − 10x = 12
3. Adding a number to both sides to complete the square: x^2 − 10x + 25 = 12 + 25
4. Factoring and simplifying: (x−5)^2 = 37
5. Take square root of both sides: x−5 = ±√37
6. Solve for x: x = 5 ± √37
7. Isolating the variable: No further steps needed
8. Final answers: x = 5 + √37 and x = 5 - √37