Question

Use the quadratic formula to determine the exact solutions to the equation.

6x2+4x−3=0

Answer 1

Explanation:

Answer 2

`\bf ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \begin{array}{llcccl} & 6 x^2& +4 x& -3\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}`


`\bf x=\cfrac{-4\pm√(4^2-4(6)(-3))}{2(6)}\implies x=\cfrac{-4\pm√(16+72)}{12} \\\\\\ x=\cfrac{-4\pm√(88)}{12}\implies x=\cfrac{-4\pm√(4\cdot 22)}{12}\implies x=\cfrac{-4\pm√(2^2\cdot 22)}{12} \\\\\\ x=\cfrac{-4\pm 2√(22)}{12}\implies x=\cfrac{2(-2\pm 1√(22))}{12}\implies x=\cfrac{-2\pm√(22)}{6}`