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The Principle of Square Roots

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.

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The Principle of Square Roots

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  1. The Principle of Square Roots Let’s consider x2 = 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 x2 = k, where k is a constant.

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

  3. 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 x2 + 10x + 4 = 0

  4. Example Solve x2 + 10x + 4 = 0 Solution x2 + 10x + 25 = –4 + 25 Adding 25 to both sides. Factoring Using the principle of square roots The solutions are

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

  6. 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%.

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