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3. * Often times we are not able to a quadratic equation in order to solve it. When this is the case, we have two other methods: completing the square and the quadratic formula. * By learning how to the we can force a quadratic expression to factor. factor complete square

4. * Steps for Solving a Quadratic by Completing the Square * 1. Add or subtract the constant term to the other side (if necessary). * 2. Check to make sure the coefficient of is. If not, factor out the coefficient of and divide both sides of the equation by this number. * 3. Take of b, square it, and add it to sides. * 4. Make the left side a square of a binomial (example: ). * 5. Simplify the right side. * 6. Take the square root of each side. (make sure to use ). * 7. Solve for x. 1 halfboth ±

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9. * The solutions of a quadratic equation in general form, when, are given by the quadratic formula:

10. * 1. Write the equation in the form * 2. Determine the values of a, b, and c. * 3. Substitute the values of a, b, and c. into the quadratic formula and evaluate the expression. * 4. The sign indicates that there are two solutions of the equation.

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