Solve for x in the following equation.
Problem 4.3b :
The equation is already set to zero.
The equation can be written as
The only way a product can equal zero is for at least one of the factors to have a value of zero :
Method 2:Completing the square
Add 60 to both sides of the equation
Divide both sides by 2:
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 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. Substitute 2 for a, 7 for b, and -60 for c in the quadratic formula and simplify.
Graph (formed by subtracting the right side of the original equation from the left side of the original equation). Graph y=0 (the x-axis). 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 4 and -7.5. This means that there are two real answers: x=4 and
The answers are 4 and These answers may or may not be solutions to the original equation. You must check the answers with the original equation.
Check these answers in the original equation.
Check the solution x=4 by substituting 4 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 by substituting 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 4 and
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