Solve for x in the following equation.
Set the equation equal to zero by subtracting 60 and adding 2x to both sides of the equation.
Method 1: Factoring
Method 2: Completing the square
Add 78 to 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 to 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, +7 for b, and -78 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.
You can see from the graph that there are two x-intercepts located at -13 and 6. This means that there are two real answers: x=-13 and Check these answers in the original equation.
Check the solution x=-13 by substituting -13 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=6 by substituting 6 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 -13 and 6.
If you would like to work another example, click on Example
If you would like to test yourself by working some problems similar to this example, click on Problem.
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