Question

3x^2+10x=-3

Answer 1

Factoring:
3x² + 10x + 3 = 0
3x² + 9x + x + 3 = 0
3x(x + 3) + 1(x+3) = 0
(x + 3)(3x + 1) = 0

x + 3 = 0 → x = -3
3x + 1 = 0 → 3x = -1 → x = -⅓


Completing the Square:
3x² + 10x + 3 = 0
x² + (10/3)x + 1 = 0
x² + (10/3)x = -1
x² + (10/3)x + (10/6)² = - 1 + (10/6)²
x² + (10/3)x + (100/36) = -1 + (100/36)
x² + (10/3)x + (25/9) = -(9/9) + (25/9)
(x + (5/3))(x + (5/3)) = (16/9)
(x + (5/3))² = (16/9)
x + (5/3) = ±√(16/9)
x + (5/3) = ±(√16/√9)
x = -(5/3) ± (4/3)
x = (-5 ± 4)/3

x = (-5 + 4)/3 = -⅓
x = (-5 - 4)/3 = -9/3 = -3


Verify the answer:
3(-⅓)² + 10(-⅓) + 3 = 3(1/9) - (10/3) + 3 = (1/3) - (10/3) + (9/3) = -(9/3) + (9/3) = 0

3(-3)² + 10(-3) + 3 = 3(9) - 30 + 3 = 27 - 30 + 3 = -3 + 3 = 0