 # Solving Using the Quadratic Formula Each time we solve by completing the square, the procedure is the same. In mathematics, when a procedure is repeated.

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Solving Using the Quadratic Formula Each time we solve by completing the square, the procedure is the same. In mathematics, when a procedure is repeated many times, a formula can often be developed to speed up our work. If we begin with a quadratic equation in standard form, ax 2 + bx + c = 0, and solve by completing the square we arrive at the quadratic formula.

Example Solution Solve 3x 2 + 5x = 2 using the quadratic formula. First determine a, b, and c: 3x 2 + 5x – 2 = 0 a = 3, b = 5, and c = –2. Substituting

Example Solution First determine a, b, and c: x 2 – 2x + 7 = 0 a = 1, b = –2, and c = 7. Solve x 2 + 7 = 2x using the quadratic formula. Substituting

Approximating Solutions When the solution of an equation is irrational, a rational-number approximation is often useful. This is often the case in real-world applications similar to those found in section 8.3. Example Solution Use a calculator to approximate Take the time to familiarize yourself with your calculator:

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