Question

In simplest radical form, what are the solutions to the quadratic equation 6 = x2 - 10%?-b IVb2 - 400Quadratic formula: x =2aO x=5+31Ox=519Ox=54219Ox=5+2/31

Answer 1

The cuadratic formula is:

`ax^2+bx+c`

Where a, b and c are coefficients.

For the given quadratic equation:

`\begin{gathered} 6=x^2-10x \\ x^2-10x-6 \end{gathered}`

The coefficients are:

`\begin{gathered} a=1 \\ b=-10 \\ c=-6 \end{gathered}`

Replace in the quadratic formula to solve:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`
`x=-(b)/(2a)\pm\frac{\sqrt[]{b^2-4ac}}{2a}`
`\begin{gathered} x=(-(-10))/(2\cdot1)\pm\frac{\sqrt[]{(-10)^2-4\cdot1\cdot(-6)}}{2\cdot1} \\ x=(10)/(2)\pm\frac{\sqrt[]{100-24}}{2} \\ x=5\pm\sqrt[]{31} \end{gathered}`

The solution for the quadratic formula is the first choice.