Question

Help to solve using quadratic formula; round to nearest hundredth

Answer 1

Given:

`6x^2\text{ - 14x - 9 = 0}`

The quadratic formula is defined as:

`x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}`

given that the general form of a quadratic equation is:

`ax^2\text{ + bx + c = 0}`

Hence:

a = 6, b = -14, c = -9

Substituting into the formula:

`x\text{ = }\frac{-(-14)\text{ }\pm\sqrt[]{(-14)^2\text{ -4(6)(-9)}}}{2*6}`

Simplifying we have:

`\begin{gathered} x\text{ = }\frac{14\text{ }\pm\text{ }\sqrt[]{412}}{12} \\ =\text{ }\frac{14\text{ }\pm\text{ }\sqrt[]{412}}{12} \\ =\text{ }\frac{14\text{ }\pm\text{ 2}\sqrt[]{103}}{12} \\ =\text{ }\frac{7\text{ }\pm\sqrt[]{103}}{6} \end{gathered}`

Answer:

`x\text{ = }\frac{7\text{ + }\sqrt[]{103}}{6}\text{ or }\frac{7\text{ - }\sqrt[]{103}}{6}`