3. The Quadratic Formula
Using the method of completing the square, we can derive a general formula for solving quadratic equations:
For any quadratic equation ax2 + bx + c = 0, the solutions for x can be found by using the quadratic formula:
Example 1:
Solve 2x2 - 7x - 5 = 0
Answer
By inspection, we can see that: a = 2, b = -7 and c = -5
Substituting these into the quadratic formula, we get :
Here is a LiveMath document to illustrate this formula.
Example 2:
Solve 2x2 = 4x + 3
Exercise
Solve 6r2 = 6r + 1 using the quadratic formula.
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