Question

Solve the equation by using the quadratic formula. Write imaginary solutions in the form atbi. Express answers in simplified form using intefractions, orradicals.N^2 +18-10The solution set is

Answer 1

`\text{The solution set is }5\pm\sqrt[]{7}`

Step-by-step explanation:
`\begin{gathered} n^2\text{ + 18 = }10n \\ n^2\text{ -10n + 18 = 0} \end{gathered}`

Using quadratic formula:

`x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`
`\begin{gathered} \text{for ax}^2\text{ + bx + c = 0} \\ \text{comparing with the given equation:} \\ a\text{ = 1, b = -10, c = 18} \end{gathered}`
`\begin{gathered} x\text{ = }\frac{-(-10)\pm\sqrt[]{(-10)^2-4(1)(18)}}{2(1)} \\ x\text{ = }\frac{10\pm\sqrt[]{100-72}}{2} \\ x\text{ = }\frac{10\pm\sqrt[]{28}}{2} \end{gathered}`

`\begin{gathered} x\text{ = 5 +}\sqrt[]{7\text{ }}\text{ or } \\ x\text{ = 5 -}\sqrt[]{7\text{ }} \\ \text{The solution set is }5\pm\sqrt[]{7} \end{gathered}`