Solve the equation by factoring: 3x² - 10x + 7 = 0(2 points) x = ,
First, we need to factor the quadratic equation:
3x² - 10x + 7 = 0
To factor, we look for two numbers that multiply to 21 (3 * 7) and add to -10. These numbers are -7 and -3.
Therefore, we rewrite the equation as:
3x² - 7x - 3x + 7 = 0
Factor by grouping:
x(3x - 7) - 1(3x - 7) = 0
(3x - 7)(x - 1) = 0
Set each factor to zero:
3x - 7 = 0 or x - 1 = 0
3x = 7 or x = 1
x = 7/3 or x = 1
Therefore, the solutions are x = 7/3 or x = 1.