Sienna is solving the quadratic equation by completing the square.
3x2 + 9x – 4 = 0
3x2 + 9x = 4
A(x2 + 3x) = 4
+130536 3x^2 + 9x - 4 = 0 move the 4 to the right side
3(x^2 + 3x) = 4 factor the left side
x^2 + 3x = 4/3 divide both sides by 3
x^2 + 3x + 9/4 = 4/3 + 9/4 complete the square
(x + 3/2)^2 = 43/12 factor the left side, simpllify the right
x + 3/2 = (+/-)sqrt(43/12) take the pos/neg square roots of both sides
x + 3/2 = (+/-) [ sqrt(43/3)] / 2 simplify the right
x = (+/-) [sqrt(43/3)/ 2 - 3/2 subtract 3/2 from both sides
