Note:
Solve for x in the following equation.
Problem 4.1c
Answer:
Solution:
The equation is already equal to zero.
Method 1: Factoring
The equation cannot be 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 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, +17 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. The x-intercepts are -16.389866919 and The answers are -16.389866919 and
Check these answers in the original equation.
Check the answer x=-16.389866919 by substituting -16.389866919 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=-0.61013308097 by substituting -0.61013308097 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 , and .
Comment: You can use the solutions to factor the original equation.
For example, since , then , and
Since , then , and
Since the product and , then we can say that This means that and are factors of
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Author:Nancy Marcus