Solving Quadratic Equations Using the Quadratic
Formula
Example
Solve using the quadratic formula: 10 - 5x2 = 6x
Solution
Step 1 Write the quadratic equation in standard form,
ax2 + bx + c = 0.
Subtract 6x from both sides of the equation.
On the left side, write the terms in
decreasing powers of x.
Step 2 Identify the values of a, b, and c. |
10-5x2 = 6x
![](./articles_imgs/1220/solvin1.gif) |
Step 3 Substitute the values of a,
b, and c into the quadratic
formula. |
![](./articles_imgs/1220/solvin2.gif) |
Step 4 Simplify. |
![](./articles_imgs/1220/solvin3.gif) |
Simplify the radical.
![](./articles_imgs/1220/solvin4.gif) |
![](./articles_imgs/1220/solvin5.gif) |
Factor -2 from the numerator
and denominator.
Reduce by canceling the
common factor, -2
Step 5 Check each solution.
We leave the check to you. |
![](./articles_imgs/1220/solvin6.gif) |
The two solutions of 10 - 5x2 = 6x are
![](./articles_imgs/1220/solvin7.gif)
Note:
Here’s another way to simplify: |
![](./articles_imgs/1220/solvin8.gif) |
Factor out 2. |
![](./articles_imgs/1220/solvin9.gif) |
Multiply by
![](./articles_imgs/1220/solvin10.gif) |
![](./articles_imgs/1220/solvin11.gif) |
(We multiplied by
because we do not
want a negative sign in the denominator.)
|