Solving Quadratic Equations Using the Quadratic
Formula
Example
Solve using the quadratic formula: 36x 2 + 16 + 48x = 0
Solution
| Step 1 Write the quadratic equation in standard form,
ax2 + bx + c = 0. |
36x2 + 16 + 48x = 0 |
| On the left side, write the terms in
decreasing powers of x.
Each term is divisible by 4. To simplify
the calculations, divide both sides of
the equation by 4.
Step 2 Identify the values of a, b, and c. |
36x2 + 16 + 48x = 0
 |
| Step 3 Substitute the values of a,
b, and c into the quadratic
formula. |
 |
| Step 4 Simplify. |
 |
| Step 5 Check each solution.
We leave the check to you.
|
|
We say that
 is a solution of multiplicity two.
Example 2
Solve using the quadratic formula: x2 + 5 = 3x
Notice the negative number under the square root symbol.
The radical
 does not represent a real number.
Therefore, the equation x2 + 5 = 3x has no real number solutions.
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