Respuesta :
Answer
The solutions for this quadratic equation is given as
[tex]w=\frac{-1\pm i\sqrt[]{59}}{6}[/tex]which can then be broken down and then written as
[tex]\begin{gathered} w=\frac{-1+i\sqrt[]{59}}{6} \\ OR \\ w=\frac{-1-i\sqrt[]{59}}{6} \end{gathered}[/tex]
Explanation
Quadratic equations of the form aw² + bw + c = 0, can be solved using the quadratic formula. The quadratic formula is given as
[tex]w=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]For this question, we still need to simplify the equation to put it in the general quadratic equation form.
3w² + w + 10 = 5
3w² + w + 10 - 5 = 0
3w² + w + 5 = 0
Comparing this to the general form aw² + bw + c = 0
a = 3
b = 1
c = 5
[tex]\begin{gathered} w=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ w=\frac{-1\pm\sqrt[]{1^2-4(3)(5)}}{2(3)} \\ w=\frac{-1\pm\sqrt[]{1-60}}{6} \\ w=\frac{-1\pm\sqrt[]{-59}}{6} \end{gathered}[/tex]Noting that the square root of a (-1) gives he complex number i
[tex]\begin{gathered} w=\frac{-1\pm\sqrt[]{-59}}{6} \\ w=\frac{-1\pm i\sqrt[]{59}}{6} \\ w=\frac{-1+i\sqrt[]{59}}{6} \\ OR \\ w=\frac{-1-_{}i\sqrt[]{59}}{6} \end{gathered}[/tex]Hope this Helps!!!
