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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.5, Problem 2E

(**a**)

To determine

**To explain:** The method of factoring to solve the equation

Expert Solution

**Property used:**

*Zero-product property:*

If

**Calculation:**

Note that, the expression on the left side of a quadratic equation in the standard form

Then, by using the zero-product property set each factor equal to zero. Then, the resulting equations are solved to obtain the given quadratic equation.

Thus, the given equation can be solved by factoring the expression

Now, use the zero-product property to find the solutions.

Thus, the solutions of equation

(**b**)

To determine

**To explain:** The method of completing the square to solve the equation

Expert Solution

**Method used:**

*Completing the square:*

1. Begin by writing the equation with the constant on the right side.

2. If the coefficient of *x* and balance it by adding the same value on the right side.

3. If the coefficient of

That is, to make *x*. This gives the perfect square

**Calculation:**

Consider the given equation

Add 5 on both the sides of equation

Here, the coefficient of *x* and balance it by adding the same value on the right side

That is, add

Add 2 on both sides of the equation to obtain the final solution.

Thus, the solution of equation

(**c**)

To determine

**To explain:** The method of using quadratic formula to solve the equation

Expert Solution

**Formula used:**

*Quadratic formula:*

The solution of a quadratic equation of the form

**Calculation:**

Consider the given equation

Compare this equation with the general form

Here

Substitute 1 for *a*, *b* and *c* in the quadratic formula to find the solution.

Simplify further as follows.

Thus, the solution of equation