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Solve by using the Quadratic Formula.
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| This equation is in standard form. |
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| Identify the a, b, c values. |
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| Write the Quadratic Formula. |
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| Then substitute in the values of a, b, c. |
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| Simplify. |
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| Rewrite to show two solutions. |
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| Simplify. |
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Check.
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When we solved quadratic equations by using the Square Root Property, we sometimes got answers that had radicals. That can happen, too, when using the Quadratic Formula. If we get a radical as a solution, the final answer must have the radical in its simplified form.
Solve by using the Quadratic Formula.
We can use the Quadratic Formula to solve for the variable in a quadratic equation, whether or not it is named ‘ x ’.
 | |
| This equation is in standard form. |
 |
| Identify the a, b, c values. |
 |
| Write the Quadratic Formula. |
 |
| Then substitute in the values of a, b, c. |
 |
| Simplify. |
 |
| Rewrite to show two solutions. |
 |
| Check. We leave the check to you. |
Solve by using the Quadratic Formula.
 | |
| This equation is in standard form. |
 |
| Identify the a, b, c values. |
 |
| Write the Quadratic Formula. |
 |
| Then substitute in the values of a, b, c. |
 |
| Simplify. |
 |
| Simplify the radical. |
 |
| Factor out the common factor in the numerator. |
 |
| Remove the common factors. |
 |
| Rewrite to show two solutions. |
 |
| Check. We leave the check to you. |
We cannot take the square root of a negative number. So, when we substitute , , and into the Quadratic Formula, if the quantity inside the radical is negative, the quadratic equation has no real solution. We will see this in the next example.
Solve by using the Quadratic Formula.
| This equation is in standard form. |
 |
| Identify the a, b, c values. |
 |
| Write the Quadratic Formula. |
 |
| Then substitute in the values of a, b, c. |
 |
| Simplify. |
 |
| Simplify the radical. |
 |
| We cannot take the square root of a negative number. | There is no real solution. |
The quadratic equations we have solved so far in this section were all written in standard form, . Sometimes, we will need to do some algebra to get the equation into standard form before we can use the Quadratic Formula.
Solve by using the Quadratic Formula.
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| Distribute to get the equation in standard form. |
 |
| This equation is now in standard form. |
 |
| Identify the a, b, c values. |
 |
| Write the Quadratic Formula. |
 |
| Then substitute in the values of a, b, c. |
 |
| Simplify. |
 |
| Simplify inside the radical. |
 |
| Simplify the radical. |
 |
| Factor out the common factor in the numerator. |
 |
| Remove the common factors. |
 |
| Rewrite to show two solutions. |
 |
| Check. We leave the check to you. |
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