This method is used to solve quadratic equations when the quadratic will not factor. ( The process of completing the square also has many other useful applications, so it is a good idea to learn how to use it.!)
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Step and Description |
Result of taking step |
| 1. If the coefficient of the quadratic term (the x2 term) is not 1, then we divide both sides of the equation by whatever it is. |
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| 2. Add + ____ to each side of the equation. |
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| 3. What we want to put in each of the two blanks is a
constant that will turn the quadratic expression into a perfect square
trinomial (hence we will be "completing the square"). Here
is how we will get that constant: - Take the linear coefficient (the multiplier of the x term) - Cut that number in half - Square that In our example problem, the linear coefficient is 13/5, so what we need to put in each of the blanks is  |
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| 4. On the one side, write the quadratic as its square
root squared, and on the other side, combine the constant terms. Note: The square root of a perfect square quadratic trinomial with leading coefficient 1 is (x + half the coefficient of the linear term). |
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| 5. Now we are almost home free. We take the
square root of both sides, and this gets us a nice linear
equation, so we can 6. Solve the linear equation for x |
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| 7. Check your answers in the original equation: 5x2 + 13x = 6
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