4. The Principle of Square Roots Let’s consider x 2 = 25. We know that the number 25 has two real-number square roots, 5 and  5, the solutions of the equation. Thus we see that square roots can provide quick solutions for equations of the type x 2 = k, where k is a constant.

6. Example Solution Solve (x + 3) 2 = 7 The solutions are

7. Completing the Square Not all quadratic equations can be solved as in the previous examples. By using a method called completing the square, we can use the principle of square roots to solve any quadratic equation. Solve x 2 + 10x + 4 = 0

8. Example Solution Solve x 2 + 10x + 4 = 0 x 2 + 10x + 25 = –4 + 25 The solutions are Using the principle of square roots Factoring Adding 25 to both sides.

12. Example Solution Jackson invested $5800 at an interest rate of r, compounded annually. In 2 years, it grew to $6765. What was the interest rate? 1.Introduction. We are already familiar with the compound-interest formula. 6765 = 5800(1 + r) 2 The translation consists of substituting into the formula:

13. 2. Body. Solve for r: 6765/5800 = (1 + r) 2 Since the interest rate cannot be negative, the solution is.080 or 8.0%. 3. Conclusion. The interest rate was 8.0%.