Note:
Solve for x in the following equation.
Problem 4.1b
Answer: x = - 8 , 4
Solution:
The equation is already equal to zero.
Method 1: Factoring
The equation can be written in the equivalent form of The only way that a product can equal zero is if one or both of the factors equal zero.
The answers are
Method 2: Completing the square
Add 32 to both sides of the equation.
Add 4 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 2 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, +4 for b, and -32 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. The x-intercepts are 4 and The answers are 4 and
Check these answers in the original equation.
Check the answer 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 x=-8 by substituting -8 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 -8.
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Author:Nancy Marcus