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}$$x=-\frac{b}{2a}\pm\frac{\sqrt[]{b^2-4ac}}{2a}$$\begin{gathered} x=\frac{-(-10)}{2\cdot1}\pm\frac{\sqrt[]{(-10)^2-4\cdot1\cdot(-6)}}{2\cdot1} \\ x=\frac{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.