Question

Rewrite the equation by completing the square. x^2-51=14x

Answer 1

We have to factorize the equation:

`\begin{gathered} x^2-51=14x \\ x^2-14x-51=0 \end{gathered}`

We apply the quadratic formula:

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-14)\pm\sqrt[]{(-14)^2-4\cdot1\cdot(-51)}}{2\cdot1} \\ x=\frac{14\pm\sqrt[]{196+204}}{2} \\ x=(14)/(2)\pm\frac{\sqrt[]{400}}{2}=7\pm(20)/(2)=7\pm10 \\ x_1=7-10=-3 \\ x_2=7+10=17 \end{gathered}`

As we find the two roots of the equation, we can rewrite the equation as:

`(x+3)(x-17)=0`