Question

Use the Square Root Property to solve the quadratic equation 36c2−144c+144=−35. If there are multiple answers, list them separated by a comma, e.g. 1,2. If there is no solution, enter ∅.

Answer 1

The square root property to solve the quadratic equation;

`\begin{gathered} 36c^2-144c+144=-35 \\ 36c^2-144c+144+35=0 \\ 36c^2-144c+179=0 \end{gathered}`

is given as;

`\begin{gathered} c=\frac{-b\pm\sqrt[]{b^2-4ad}}{2a} \\ \\ \text{Where} \\ a=36 \\ b=-144 \\ d=179 \end{gathered}`
`\begin{gathered} c=\frac{-(-144)\pm\sqrt[]{(144)^2-4(36)(179)}}{2(36)} \\ c=\frac{144\pm\sqrt[]{-5040}}{72} \\ \end{gathered}`
`\begin{gathered} \text{Since,} \\ \sqrt[]{b^2-4ad}<0 \\ \text{Then, th}ere\text{ is no real solution for c} \\ c=\phi \end{gathered}`