   Chapter A.4, Problem 32E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 25 to 32, solve each quadratic equation by factoring. 12 x 2 + 10 x = 12

To determine

To solve:

The quadratic equation by factorization.

12x2+10x=12

Explanation

Solving an equation is to find the value of the unknown variables in the equation, such that the obtained value or values of the unknown should satisfy the equation from which it was derived. Such a value is said to be the solution for the equation. In general a quadratic equation has two solutions for the variable in the equation as the degree of the equation is two.

Calculation:

Given,

12x2+10x=12

The above equation is not in the standard form of a quadratic equation.

Add; -12 on both side,

12x2+10x+-12=12+-12

12x2+10x-12=0

Now, we shall proceed with the factorization of the quadratic expression in the left of the equation.

First look for the common factor GCF of the terms 12x2, 10x and -12.

But, here the GCF is 2.

Here, divide each term of the given equation by 2 on both sides.

12x22+10x2-122=0

6x2+5x-6=0

Now, factor the expression 6x2+5x-6 by reverse FOIL method.

First factorize the product of the coefficient of the first tern and the constant, such that the sum of the factors gives the coefficient of the middle term.

Thus, factorize -36 as 9·-4 so that the sum of the factors 9+(-4) gives +5.

Now, split the middle term 5x as 9x+(-4x).

Hence, the given equation becomes

6x2+9x+-4x-6=0

3x·2x+3x·3+2x·-2+3·-2=0

Factor out the common factors form the first two terms and form the last two terms of the above expression.

3x·2x+3+-22x+3=0

Here, 2x+3 is distributed over 3x+(-2)

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