Find all solutions to the equation 6x^2 - 31x + 42 = 0. If you find more than one, then list the values separated by commas. If the solutions are not real, then they should be written in a + bi form.
+515 Lets solvie this:
\(6x^2-31x+42=0\)
\(\frac{-\left(-31\right)\pm \sqrt{\left(-31\right)^2-4\cdot \:6\cdot \:42}}{2\cdot \:6}\)
\(\frac{-\left(-31\right)\pm \sqrt{47}i}{2\cdot \:6}\)
separate: \(x_1=\frac{-\left(-31\right)+\sqrt{47}i}{2\cdot \:6},\:x_2=\frac{-\left(-31\right)-\sqrt{47}i}{2\cdot \:6}\)
\(x=\frac{31}{12}+\frac{\sqrt{47}}{12}i,\:x=\frac{31}{12}-\frac{\sqrt{47}}{12}i\)
+515 Lets solvie this:
\(6x^2-31x+42=0\)
\(\frac{-\left(-31\right)\pm \sqrt{\left(-31\right)^2-4\cdot \:6\cdot \:42}}{2\cdot \:6}\)
\(\frac{-\left(-31\right)\pm \sqrt{47}i}{2\cdot \:6}\)
separate: \(x_1=\frac{-\left(-31\right)+\sqrt{47}i}{2\cdot \:6},\:x_2=\frac{-\left(-31\right)-\sqrt{47}i}{2\cdot \:6}\)
\(x=\frac{31}{12}+\frac{\sqrt{47}}{12}i,\:x=\frac{31}{12}-\frac{\sqrt{47}}{12}i\)
