Note:
Example 4:
The equation is already equal to zero.
Method 1: Factoring
We will not use this method because the left side of the equation is not easily factored.
Method 2: Completing the square
Subtract 10 from both sides of the equation.
Add to both sides of the equation.
Factor the left side and simplify the right side.
Take the square root of both sides of the equation,
Subtract 3 from both sides of the equation.
Method 3: Quadratic Formula
The quadratic formula is .
In the equation , a is the coefficient of the term, b is the coefficient of the x term, and c is the constant. Simply insert 1 for a, 6 for b, and 10 for c in the quadratic formula and simplify.
Method 4: Graphing
Graph y= the left side of the equation or and graph y= the right side of the equation or y=0. The graph of y=0 is nothing more than the x-axis. So what you will be looking for is where the graph of crosses the x-axis. Another way of saying this is that the x-intercepts are the solutions to this equation. There are no x-intercepts. This means that there are no real solutions; the only solutions will be imaginary. The answers are -3+i and
Check these answers in the original equation.
Check the answer x=-3+i by substituting -3+i in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.
Check the solution x=-3-i by substituting -3-i in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.
The solutions to the equation are
x = - 3 - i and - 3 + i.
Comment: You can use the solutions to factor the original equation.
For example, since x=-3-i, then
Since x=-3+i, then
Since the product and , then we can say that This means that and are factors of
If you would like to test yourself by working some problems similar to this example, click on Problem.
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Author:Nancy Marcus