Final answer:
To solve the equation x^2 - 8x + 14 = 2x - 7x, rearrange it into a quadratic equation and use the quadratic formula to find the solutions.
Step-by-step explanation:
To solve the equation x^2 - 8x + 14 = 2x - 7x:
- Rearrange the equation to convert it into a quadratic equation: x^2 - 8x + 14 - 2x + 7x = 0
- Simplify the equation: x^2 - 3x + 14 = 0
- Use the quadratic formula to find the solutions of the equation:
- x = (-(-3) ± √((-3)^2 - 4(1)(14))) / (2(1))
- x = (3 ± √(9 - 56)) / 2
- x = (3 ± √(-47)) / 2
- x = (3 ± i√47) / 2