Add the number that would make the expression a perfect square. Next, write an equivalent expression in factored form.

1. \(x^2 + 3x\)
2. \(x^2 + 0.6x\)
3. \(x^2 - 11x\)
4. \(x^2 - \frac52 x\)
5. \(x^2 + x\)

Noah is solving the equation \(x^2 + 8x + 15 = 3\). He begins by rewriting the expression on the left in factored form and writes \((x+3)(x+5)=3\). He does not know what to do next. 

Noah knows that the solutions are \(x= \text- 2\) and \(x = \text- 6\), but is not sure how to get to these values from his equation. 

Solve the original equation by completing the square. 

An equation and its solutions are given. Explain or show how to solve the equation by completing the square.

1. \(x^2 + 20x + 50 = 14\) . The solutions are \(x = \text- 18\) and \(x = \text- 2\).
2. \(x^2 + 1.6x = 0.36\) . The solutions are \(x = \text- 1.8\) and \(x = 0.2\).
3. \(x^2 - 5x = \frac{11}{4}\). The solutions are \(x = \frac{11}{2}\) and \(x = \frac{\text- 1}{2}\).