Question

Solve w2+13w=20 by completing the square. If there are multiple answers, list them separated by a comma (e.g., 1,2). If there is no solution, enter ∅.

Answer 1

Answer:

w = -14.39, 1.39

Explanations:

The given quadratic equation is:

`w^2+13w=20`

Add (13/2)² to both sides of the equation

`\begin{gathered} w^2+13w+((13)/(2))^2=20+((13)/(2))^2 \\ (w+(13)/(2))^2=\text{ 20+}(169)/(4) \\ (w+(13)/(2))^2=\text{ }(249)/(4) \\ w+(13)/(2)=\pm\text{ }\sqrt[]{(249)/(4)} \\ w\text{ = }(-13)/(2)\pm\sqrt[]{(249)/(4)} \end{gathered}`
`\begin{gathered} w\text{ = -6.5}\pm7.89 \\ w\text{ = -6.5+7.89 = }1.39 \\ w\text{ = -6.5-7.89 = }-14.39 \end{gathered}`

w = -14.39, 1.39