Write an equation that defines m (x) as a trinomial where m (x) = (3x - 1) (3 - x) + 4x^2 + 19.

Solve for x when m (x) = 0.

M (x) = (3x - 1) (3 - x) + 4x^2 + 19

0 = 9x - 3x^2 - 3 + x + 4x^2 + 19

0 = x^2 + 10x + 16

now use quadratic formula

a = 1 b = 10 c = 16

x = - b + / - √b²-4ac : 2a

x = - 10 + / - √100 - 4 (16) : 2

x = - 10 + / - √100-64 : 2

x = - 10 + / - √36 : 2

split the equation

x = - 10 - 6 : 2 and x = - 10 + 6 : 2

x = - 16 : 2 x = - 4 : 2

x = - 8 x = - 2

so the value for x are - 8 and - 2

M (x) = (3x - 1) (3 - x) + 4x² + 19

0 = 3x (3 - x) - 1 (3 - x) + 4x² + 19

0 = 3x (3) - 3x (x) - 1 (3) + 1 (x) + 4x² + 19

0 = 9x - 3x² - 3 + x + 4x² + 19

0 = - 3x² + 4x² + 9x + x - 3 + 19

0 = x² + 10x + 16

x = - (10) ± √ ((10) ² - 4 (1) (16))

2 (1)

x = - 10 ± √ (100 - 64)

2

x = - 10 ± √ (36)

2

x = - 10 ± 6

2

x = - 5 ± 3

x = - 5 + 3 U x = - 5 - 3

x = - 2 U x = - 8